Brain Physiology, Cognition and Consciousness: notice board entry
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Waves of Excitation
- Posted by:
- Alfredo Pereira Jr (group admin)
- Date:
- 24 August 2007
- Comments:
- 25 comments
How these waves (below) impact on current hypotheses about brain
correlates of consciousness?
The Neuron Doctrine is challenged…
After this result, will Walter Freeman’s work be accepted by
mainstream neuroscience?
Best Regards,
Alfredo Pereira Jr.
For the first time, patterns of excitation waves found in brain’s
visual processing center
Neuroscientists have long believed that vision is processed in the
brain along circuits made up of neurons, similar to the way telephone
signals are transferred through separate wires from one station to
another. But scientists at Georgetown University Medical Center
discovered that visual information is also processed in a different
way, like propagating waves oscillating back and forth among brain
areas. Their findings are published in the July 5 issue of the
journal Neuron.
“What we found is that signals pass through brain areas like
progressive waves, back and forth, a little bit like what fans do at
baseball games,” said the study’s corresponding author, Jian-Young
Wu, Ph.D., an associate professor in the Department of Physiology and
Biophysics at Georgetown. Just as the stadium wave is coordinated and
travels through the crowd, a collective pattern emerges from the
activities of millions of neurons in the visual areas, he said,
explaining, “It simply makes sense that brain function is the result
of large numbers of neurons working together.”
This challenges longstanding notions about how the brain processes
sensory information, Wu said. “One traditional model theorizes that
neurons are hooked together into specific circuits. However, new
imaging methods tell us that there are more than just circuits.”
Wu and his colleagues visualized wave-like patterns in the brain
cortex using a new method called voltage sensitive dye imaging. They
used a special dye that binds to the membrane of neurons and changes
color when electrical potential passes along active neurons.
Traditionally, scientists have studied brain activity by placing
electrodes in the brain and measuring the electrical currents that
are related to neuronal activity. Because it is difficult to put many
electrodes into the brain, the spatiotemporal pattern of the neuronal
activity has long been ignored. “Now, with optical methods, we can
watch sequential activation of different sectors of the visual cortex
when the brain is processing sensory information,” Wu said.
Wu believes wave patterns play an important role in initiating and
organizing brain activity involving millions to billions of neurons.
A few years ago, Wu’s imaging group uncovered spiraling waves
resembling little hurricanes in animal epilepsy models. Wu thinks
that through this hurricane-like spiral pattern, a small area of
damaged neural tissue can generate a powerful storm that invades
large normal brain areas and starts a seizure attack. This hypothesis
would mean that disorders such as epilepsy could be viewed not just
as mis-wiring in the brain, but as an abnormal wave pattern that
invades normal tissue.
Finding waves during visual processing is an important step toward
understanding how the brain processes sensory information, explained
Wu. This understanding has the potential to help scientists
understand the abnormal waves that are generated in the brains of
patients with Parkinson’s disease and epilepsy, and how the mind
fails when the brain of an Alzheimer’s disease patient cannot
properly organize population neuronal activity, he said.
Wu believes that additional research is needed in order to understand
both normal and abnormal waves in the human brain. “Understanding how
the brain handles these waves will provide further insight into the
functioning of one of the most complex systems in the universe,” he
said.
Thanks to Alfredo Pereira for this exciting news.
I would like to reiterate my view that synchrony in neural excitation ought to facilitate the build-up of perceptual images via superposition of photons.
On a mind/brain identity theory, perceptual fields are most plausibly photon fields, which mediate all electrochemical activity in the brain and which superpose as bosons, thus allowing us to recover the basic phenomenology of sight & sound, e.g.
“To monochromatic light corresponds in the acoustic domain the simple tone. Out of different kinds of monochromatic light composite light may be mixed, just as tones combine to a composite sound. This takes place by superposing simple oscillations of different frequency with definite intensities.” (Weyl)
With a nod to Fourier, we can then build up any wave form whatever by further superpositions—thus recovering any image we might see or hear.
Finally, we can model all higher-order processes by employing the tensor network theory of Pellionisz & Llinas, wherein neural nets act as tensor operators on wave/vectors, in keeping with Heisenberg’s matrix formulation of quantum mechanics.
All of these processes can only occur if the relevant photons arrive at the same place and at the same time—or, in sync—for otherwise those photons would not faithfully map the external world.
Looking back, it seems to me, given the feedback I’ve received, that these rather obvious results have been rendered obscure by the widespread notion that the brain’s EM fields are the sorts of things EEGs record—which are only very gross, global sorts of fields. It is therefore crucial to point out that, according to QED, all chemical processes are mediated by photons and electrons—by electrons exchanging photons. See, e.g., Feynman and Salam:
“I would like to again impress you with the vast range of phenomena that the theory of quantum electrodynamics describes: It’s easier to say it backwards: the theory describes all the phenomena of the physical world except the gravitational effect [...] and radioactive phenomena, which involve nuclei shifting in their energy levels. So if we leave out gravity and radioactivity (more properly, nuclear physics) what have we got left? Gasoline burning in automobiles, foam and bubbles, the hardness of salt or copper, the stiffness of steel. In fact, biologists are trying to interpret as much as they can about life in terms of chemistry, and as I already explained, the theory behind chemistry is quantum electrodynamics.” (Feynman, QED)
“all chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses.” (Salam, Unification of Fundamental Forces)
At the risk of belaboring the obvious, it seems to follow as a ready consequence that, if conscious processes are “phenomena of nerve impulses,” then conscious processes are “electromagnetic in origin.”
Flanagan, Brian Are Perceptual Fields Quantum Fields?
Dear Brian:
While most quantum consciousness theorists have related the conscious state with the collapse of the wavefunction, you are the true and original theorist who identified it with photonic fields. Recent results concerning excitatory electric waves and synchrony supporting consciousness suggest that coherent neuronal activity generates another wave, which is not measured by the EEG.
Karl Phibram said, in his recent conference at the Quantum Mind 2007 meeting in Salzburg, that consciousness is not the electric wave, but a second-order kind of phenomenon: the interference patterns of the waves.
In my recent modeling (still unpublished), I propose that such interference patterns impact on another kind of wave: calcium ion waves in astrocytes. But, again, the phonon patterns formed by populations of calcium ions are just complex photonic fields; possibly, the most coherent, integrated and informationally rich fields in the brain.
Best Regards,
Alfredo
Dear Alfredo,
While most quantum consciousness theorists have related the conscious state with the collapse of the wavefunction, you are the true and original theorist who identified it with photonic fields.
Thanks very much for your kind remarks! Credit must be given to Michael Lockwood for his work on this idea; he and I arrived at this position at about the same time and wholly independently of one another, following up on arguments from the Gestatltists and Bertrand Russell:
“Take some range of phenomenal qualities. Assume that these qualities can be arranged according to some abstract n-dimensional space, in a way that is faithful to their perceived similarities and degrees of similarity—just as, according to Land, it is possible to arrange the phenomenal colors in his three-dimensional color solid. Then my Russellian proposal is that there exists, within the brain, some physical system, the states of which can be arranged in some n-dimensional state space [...] And the two states are to be equated with each other: the phenomenal qualities are identical with the states of the corresponding physical system.”
- Lockwood, Mind, Brain and the Quantum: The Compound ‘I’
Recent results concerning excitatory electric waves and synchrony supporting consciousness suggest that coherent neuronal activity generates another wave, which is not measured by the EEG.
Karl Phibram said, in his recent conference at the Quantum Mind 2007 meeting in Salzburg, that consciousness is not the electric wave, but a second-order kind of phenomenon: the interference patterns of the waves.
Yes, the interference patterns of EPR-complete, self-referential EM waves is, I believe, what we experience as consciousness in all its manifestations—it is, to use Weyl’s pregnant phrase, “light beholding itself.”
Pribram must also be acknowledged as one of the pioneers in this field of research. In his classic modern text on Brain & Perception, he writes:
“The text of this volume claims that the mathematical formulations that have been developed for quantum mechanics and quantum field theory can go a long way toward describing neural processes due to the functional organization of the cerebral cortex.”
In my recent modeling (still unpublished), I propose that such interference patterns impact on another kind of wave: calcium ion waves in astrocytes. But, again, the phonon patterns formed by populations of calcium ions are just complex photonic fields; possibly, the most coherent, integrated and informationally rich fields in the brain.
Yes, the photonic field must couple to the brain’s “masslike” fields in order to effect behavior and the ions present a most plausible site for that coupling.
All the best,
Brian Flanagan
Lockwood was hardly the first to articulate this point of view. Feigl did so, in very similar terms, decades earlier. However, it should be clear that all identity theories are inadequate. They offer no explanation and amount to pinning tails to donkeys. Further, any claim that higher order phenomena manifests anything that is not functionally dependent upon lower orders is an appeal to magic and has no scientific merit.
Dear Steven:
Welcome to the group!
Could you please give me a reference for Feigl’s concept of consciousness as identical to photonic fields in the brain?
I would like to discuss your remark about “magic”. The expression “functionally dependent” may be interpreted as expressing that the relation between lower and higher order phenomena is deterministic (or, in the context of E. Nagel’s theory of scientific explanation – in the book “The Structure of Science” – that the explanation has a deductive form).
Are you assuming, like J. Kim, that physicalism must be reductionist?
If this is the case, do you think determinism/reductionism are compatible with C.S. Peirce’s philosophy? (In my limited knowledge of Peirce, I would say that for him the process of creating new habits is not deterministic, and the logical form of a good scientific explanation is inductive or abductive, not deductive).
Best Regards
Alfredo Pereira Jr.
I said ‘similar’ Feigl’s “The Mental and the Physical” is online at: http://ditext.com/feigl/mp/mp.html
Though I was thinking of his remarks in his paper concerning Carnap in “The Philosophy of Rudolf Carnap.”
Determinism is a broadly misunderstood term. I like Kaufmann’s “adjacent possible.” I don’t think we should be afraid of determinism especially since it is clear that the range of the possible is broader than generally considered in the 19th century.
I’m a constructionist more than I am a reductionist – but once you have a constructive model that is sufficiently comprehensive reduction within it is a necessity but if the reduction fails then it is the construction that must be reconsidered. Physicalism is not materialism, if that is what you mean (materialism appears to tolerate reductions that fail).
As you know, I read Peirce – but I don’t think I know the answer to your question. I’ve often argued that he he was predisposed to naturalistic solutions, if that is what you mean.
With respect,
Steven
Carnap, and Reichenbach too, can be found saying similar things BTW - Carnap as far back as the Aufbau (1928). Note that his physicalism differs from Feigl in that he was a clear critic of identity theory. The article I was thinking of is Feigl’s “Physicalism and the Unity of Science” in Schlipp’s “The Philosophy of Rudolf Carnap.”
Dear Steven:
Yes you wrote “similar”, thank you for the clarification.
My intention in the previous message was to stress that B. Flanagan together with M. Lockwood are the true and original authors of the idea that consciousness is (or is based on) a photonic field. For me, the most important part of the statement was not the identity of consciousness with brain activity, but the relation of consciousness with photonic fields (quantum coherent states) instead of collapsed states.
Your comment brought me good news – the possibility of a constructionist or constructivist approach to the mind/brain that conceives determinism in the context of a complex system. I confess that this possibility has not occurred to me before. I have always thought of determinism in its classical Laplacian formulation, which applies to simple (one or two-body) systems following a small set of rules (the three Laws of Newtonian mechanics).
Philosophically I classify myself as a Non-Reductive Physicalist. I agree with you that this position is different from materialism, since it allows the existence of different levels of organization in the physical world, some of them composed of energy and information only.
This position seems to be closer to Carnap than Feigl.
If convenient, please bring some Pericean remarks to our discussion!
Best Regards,
Alfredo
I don’t think Carnap would have thought of himself as a non-reductive physicalist – I’m not even sure that such a notion makes any sense, in fact, I am confident that my interpretation of it does not.
Reduction for Carnap and most neopositivists, including myself, is necessarily within the context of a logical construction. A reduction that fails does not lead to “non-reduction” – it simply leads to a reconsideration of the construction. More important, it does NOT lead to any supernatural notion – which is what “non-reductive physicalist” suggests to me.
With respect,
Steven
In fact, of course, it is worth observing that this is precisely why identity theory fails. It accepts a reduction that fails.
With respect,
Steven
Steven wrote:
I don’t think Carnap would have thought of himself as a non-reductive physicalist
Alfredo – I wrote “closer”.
Steven:
Reduction for Carnap and most neopositivists, including myself, is necessarily within the context of a logical construction. A reduction that fails does not lead to “non-reduction” – it simply leads to a reconsideration of the construction.
Alfredo – In my view, in the explanation of consciousnes we should move beyond the deductive view of explanation (Ernest Nagel, Structure of Science). Peirce and Carnap could help us with their inductive/abductive approaches.
In a non-deductive approach, there is a third alternative to “deducing X not deducing” one theory from another one. The alternative is finding a similarity between them (this idea of reasoning by similarity comes from Peter Gärdenfors’ book Conceptual Spaces).
Steven:
More important, it does NOT lead to any supernatural notion – which is what “non-reductive physicalist” suggests to me.
Alfredo – “Non-reductive” only means that one level of organization of physical reality does not reduce (in the sense advanced by E. Nagel’s paradigm of scientific explanation) to another one. John Bickle has done a very good job of softening the Nagelian paradigm, although he refers to his enterprise as “ruthless reductionism”.
I imagined that as a constructivist or constructionist you would not espouse the deductive view of scientific explanation.
Best Regards,
Alfredo Pereira Jr.
Abduction does not permit supernatural explanation – and any claim that reduction fails leaves you with only one of two options. Either the explanation is supernatural – because that is what the failure of reduction logically implies – or the constructive framework in which the reduction was made needs to be reconsidered. Penrose, and Carnap before him, essentially take the latter position, as do I.
I don’t see how it is possible to exclude deduction from scientific explanation. Deduction is the principal means of explanation in frameworks of formal logic. Therefore, it is the primary mechanism of prediction in formal explanation. So if you want to communicate your abductive and inductive insights, and provide “scientific” explanation, you had better have command of it. But it is worth adding at this point the the logical frameworks may need some refinement when we deal with questions of apprehension and learn more about the nature of perception since these deal with the foundations of logic. These are questions that I address in my own work.
With respect,
Steven
BTW: I distinguish pragmatic explanation as the process by which we work toward the ultimate constructive explanation. As long as we acknowledge that certain explanations are useful, approximations of the way things are, and we do not allow them to exclude consideration of the way things really are I have no problem.
So the empirical observations we make in cognitive and neuroscience are fundamentally important – and the empirical explanation they provide essential – I equate the work we have done and are doing in this area as analogous to the work of Kepler and Galileo before Newton – but as interesting as they are, they provide no justification for accepting identity theory.
With respect,
Steven
Dear Steven:
It seems to me that you answered your own objection. Pragmatic explanation is the alternative to deduction. In a pragmatic explanation, it is possible to support a conclusion with similarities, analogies and approximations.
If the world is Cournotian (as I believe it is) the meeting of independent causal lines produces new, unpredictable phenomena. We can not, in principle, deduce such phenomena from our knowledge of the antecedents (even if we were omniscient beings).
The Cournotian picture seems to apply to the evolution of complex chaotic systems. These systems are defined in a deterministic framework, but determinism is lost once their independent sub-systems interact.
Prigogine developed interesting thoughts on this subject, but he assumed that the world is probabilistic at the fundamental level, and therefore the indeterministic implication was trivial.
I do not agree with a full brain-mind identity theory either. The only version I accept is a partial one, that equates one aspect of consciousness with one aspect of brain activity. This view is consistent with the proposed pragmatic explanation of (one aspect of) consciousness from (one aspect of) brain activity.
Best Regards
Alfredo
No, you are mistaken. Pragmatics is not an alternative to deduction.
Pragmatics may indeed be based on deduction from incomplete data. Pragmatics are merely useful predictions from observation – in medicine, for example. You are very confused if you really think that pragmatics is an alternative to deduction. You are even more confused if you think that deduction is something disconnected from a specific logical framework.
You must have a clear and formal reference to discuss deduction (afterall, deduction is the stuff of analysis and convention) . Otherwise you are talking about some nebulous notion of deduction that I do not understand.
With respect,
Steven
And BTW, you are appealing to the supernatural again. That, I simply cannot accept.
Thanks to Ericsson-Zenith for his equitable remarks, characteristically free of dogmatic assertions.
I quoted Feigl at the outset of my paper, Are Perceptual Fields Quantum Fields?
The solution that appears most plausible to me, and that is consistent with a thoroughgoing naturalism, is an identity theory of the mental and the physical, as follows: Certain neuro-physiological terms denote (refer to) the very same events that are also denoted (referred to) by certain phenomenal terms. The identification of the objects of this twofold reference is of course logically contingent, although it constitutes a very fundamental feature of our world as we have come to conceive it in the modern scientific outlook. Using Frege’s distinction between Sinn (‘meaning’, ‘sense’, ‘intension’), and Bedeutung (‘referent’, ‘denotatum’, ‘extension’), we may say that neurophysiological terms and the corresponding phenomenal terms, though widely differing in sense [...] do have identical referents. I take these referents to be the immediately experienced qualities, or their configurations in the various phenomenal fields.
“Mind-body, not a pseudo problem” Feigl, Herbert. The Mind-Brain Identity Theory. Borst, CV, ed. New York, NY: St. Martin’s Press, 1970.
Following up on Russell and the Gestaltists, Lockwood and I sharpened “neuro-physiological terms” to “EM terms,” as it were. As Lockwood said (private communication), I took the further step of identifying the secondary qualities with the “hidden variables” (HVs) of EPR, Bohm et al.
In more recent work, I have expanded upon that identification, pointing to:
1)the family resemblance that obtains between HVs, the “internal spaces” of gauge theory and the additional spatial dimensions of string/M-theory (as noted by Witten, e.g.); and
2) the symmetries and phase relations of color and sound; and
3) the projective character of these qualities; and
4) the fact that the secondary qualities (SQs) appear to fiber over space-time as given in perception; and
5) the fact that the SQs reliably co-vary with photonic energies; and
6) the fact that symmetries and phase relations noted in #2 are easily captured by Hamiltonians and Lagrangians (by means of the energy operator) in such a way that
7) Heisenberg’s matrix mechanics is preserved and extended in a natural way.
(Arguments re: 6 & 7 are in press.)
Steven wrote:
>Pragmatics may indeed be based on deduction from incomplete data. Pragmatics are merely useful predictions from observation – in medicine, for example. You are very confused if you really think that pragmatics is an alternative to deduction.
Alfredo – Please let me know why I am confused. Pragmatics can be based on induction and/or abduction providing rational support for logical inference. Why do you think that only deduction is valid for scientific explanation?
Steven:
You are even more confused if you think that deduction is something disconnected from a specific logical framework.
Alfredo:
I did not write or imply such a monstruosity.
Steven
You must have a clear and formal reference to discuss deduction (afterall, deduction is the stuff of analysis and convention) . Otherwise you are talking about some nebulous notion of deduction that I do not understand.
Alfredo
Why are you arguing against my knowledge of deduction? I took graduate courses on Formal Logic, Natural Deduction, etc. but this is not the issue here.
I gave a classical reference for the discussion of deduction in the context of scientific explanation: Ernest Nagel, The Structure of Science.
Also I gave references of alternative approaches: C.S.Peirce (the process of forming new habits), R.Carnap (The Logical Construction of the World; check for “Recollection of Similarity”), P.Gärdenfors (in Conceptual Spaces: the Geometry of Thought; check for “reasoning by similarity”). I could add W. Salmon’s approach to statistical explanation (in Scientific Explanation and the Causal Structure of the World).
Steven:
And BTW, you are appealing to the supernatural again. That, I simply cannot accept.
Alfredo:
What is supernatural in Cournot’s theory of chance?
Best Regards,
Alfredo
Brian wrote:
Following up on Russell and the Gestaltists, Lockwood and I sharpened “neuro-physiological terms” to “EM terms,” as it were. As Lockwood said (private communication), I took the further step of identifying the secondary qualities with the “hidden variables” (HVs) of EPR, Bohm et al.
Alfredo
Your autorship in this area is crystal-clear.
Brian
In more recent work, I have expanded upon that identification, pointing to:
1)the family resemblance that obtains between HVs, the “internal spaces” of gauge theory and the additional spatial dimensions of string/M-theory (as noted by Witten, e.g.); and
2) the symmetries and phase relations of color and sound; and
3) the projective character of these qualities; and
4) the fact that the secondary qualities (SQs) appear to fiber over space-time as given in perception; and
5) the fact that the SQs reliably co-vary with photonic energies; and
6) the fact that symmetries and phase relations noted in #2 are easily captured by Hamiltonians and Lagrangians (by means of the energy operator) in such a way that
7) Heisenberg’s matrix mechanics is preserved and extended in a natural way.
(Arguments re: 6 & 7 are in press.)
Alfredo
These hypotheses are really able to conciliate ‘qualia’ with contemporary physics.
If they lead to mind-brain identity, and how they apply to the brain, are open questions that this group can explore.
Best Regards
Alfredo
Alfredo
These hypotheses are really able to conciliate ‘qualia’ with contemporary physics.
Brian
I like to begin with sensory qualities and, more particularly, color. We ought then to be able to build up all qualia via superposition.
Contemporary physics is highly geometrical and color is geometrical in an obvious way: As children, we easily learn to identify red circles, blue squares and so on.
Contemporary physics also concerns fields in a fundamental way, and we often speak of the visual field:
“A speck in the visual field, though it need not be red must have some colour; it is, so to speak, surrounded by colour-space. Notes must have some pitch, objects of the sense of touch some degree of hardness, and so on.” (Wittgenstein)
How might we model Wittgenstein’s observations? Specifically, how can we capture the fact that “A speck in the visual field, though it need not be red must have some colour”?
A “speck in the visual field” may be any color, and it may be a different color from any of its neighbors. What we need, by way of mathematical technology, is fiber bundle theory, where copies of one kind of space “fiber over” (“sit over”) every point of space-time, e.g.
Thus, we can reproduce Wittgenstein’s piece of phenomenology by assigning a copy of color space to every “point” of the visual field.
Now, as Weyl tells us, colors define a projective vector manifold. As Maxwell and Feynman tell us, we can produce any color from three “generators,” as when we use RGB phosphors to produce all the metamers we see on our TV & computer screens. In doing so, we assign a “weight” to each of the RGB vectors.
If we use RGB vectors as the principal axes of a unit sphere, we then have a weighted, complex, projective vector manifold, fibering over the space-time of visual perception.
And this is kind of interesting, given the prominence of such manifolds in both gauge theory and Calabi-Yau theory.
(Given that Weyl established an isomorphism between colors and projective geometry, the dualities that arise in the latter field take on added interest.)
Alfredo
If they lead to mind-brain identity, and how they apply to the brain, are open questions that this group can explore.
Brian
I tend to agree with Einstein where he writes that our theories must be judged as a whole.
In the present context, mind/brain identity makes the most sense to me in respect of all I know about physics, biology, mathematics and philosophy. It both supports, and is supported by, numerous considerations drawn from all these fields.
To paraphrase another slightly: What can one do with a dualism that I cannot do with a sufficiently enriched monism?
As a psychiatrist the mind-brain problem is an everyday enigmatic problem for me, I am expected to help suffering from mind problems without knowing anything about its brain correlates, I hope that by 2050 we can resolve this as I write in my book “Optimizers 2050”:http://neuroanalysis.googlepages.com/optimizers
oops optimizers
Dear Avi:
Psychiatrists will benefit from the kind of discussion you are proposing. Today they are too dependent on prescription of drugs.
Alfredo
Returning to the notice, a new discovery (below) may help to elucidate the findings.
Alfredo
Science 319 (5871):1845-1849, 28 March 2008. [DOI: 10.1126/science.1154330]
Electric Fields Due to Synaptic Currents Sharpen Excitatory Transmission
Sergiy Sylantyev, Leonid P. Savtchenko, Yin-Ping Niu, Anton I. Ivanov,
Thomas P. Jensen, Dimitri M. Kullmann, Min-Yi Xiao, and Dmitri A.
Rusakov (28 March 2008)
The synaptic response waveform, which determines signal integration
properties in the brain, depends on the spatiotemporal profile of
neurotransmitter in the synaptic cleft. Here, we show that
electrophoretic interactions between AMPA receptor–mediated excitatory
currents and negatively charged glutamate molecules accelerate the
clearance of glutamate from the synaptic cleft, speeding up synaptic
responses. This phenomenon is reversed upon depolarization and
diminished when intracleft electric fields are weakened through a
decrease in the AMPA receptor density. In contrast, the kinetics of
receptor-mediated currents evoked by direct application of glutamate
are voltage-independent, as are synaptic currents mediated by the
electrically neutral neurotransmitter GABA. Voltage-dependent temporal
tuning of excitatory synaptic responses may thus contribute to signal
integration in neural circuits.