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Cooperative Extension Publications. Home Copyright. Focusing both eyes on a single object farther away, the development of depth perception and hand-eye coordination all take more time. Brightness and movement are visible at any distance. But regular eye exams, starting as early as two weeks of age, can detect problems that, if left uncorrected, can cause a weak or unused eye to lose its functional connections to the brain.
Vision needs to be exercised early on for good development. Visual acuity develops from birth to about age 6 or 7; binocular vision develops between ages 1 and 3. Feelings Some of the first circuits the brain builds are those that govern the emotions. The first two emotions are opposites: feeling calm and relaxed and feeling distress and tension.
Beginning around two months of age, these start to evolve into more complex feelings. Neglecting a baby can cause brain-wave patterns that dampen happy feelings. Abuse can produce anxiety, excessive stress, and can actually damage the developing brain.
Emotions develop in layers, each more complex than the last. The stress response develops immediately, from birth through age 3; empathy and envy begin to develop during the second year through about age During the first six years, its brain will set up the circuitry needed to understand and reproduce complex language.
A six-month-old can recognize the vowel sounds that are the basic building blocks of speech. Neurons grow longer dendrites and axons, which allow them to make more connections, or synapses, with other cells. The number and density of synapses increase rapidly during the first years of life. Maintaining that many synapses would demand far too much energy and other resources, however. So, during early childhood, the brain begins to pare back synapses and fine-tune the connections.
Experience — sensory stimulation and interactions with caregivers and their environment — drive this synaptic pruning process as toddlers grow. Just as pruning rose bushes gets rid of weaker branches to allow nutrients to go to the stronger branches, synaptic pruning culls weaker connections while helping more active synapses grow and stabilize. That still allows for plenty of growth and change during childhood, adolescence, and early adulthood.
Adapted from the 8th edition of Brain Facts by Jill Sakai. Dekaban, A. Changes in brain weights during the span of human life: Relation of brain weights to body heights and body weights. Annals of Neurology, 4 4 , — Fu, M. Experience-dependent structural plasticity in the cortex. Trends in Neurosciences, 34 4 , — Giedd, J. The teen brain: Insights from neuroimaging. Adolescent neuroscience of addiction: A new era. Second, at "deeper" levels of the cascade, corresponding to more stable strong and weak states, the transitions to even deeper levels corresponding to even more stable states, and the transitions in synaptic weight value from strong to weak or weak to strong, all become increasingly improbable, so that synapses in deeper cascade states remain stable over longer and longer time scales.
With this many levels, the most labile synapses at the top of the cascade change weight with probability 1 i. These two operating principles of the Cascade model are clearly distinguishable from those governing synaptic plasticity in our model. First, in the Cascade model, all synaptic state transitions are probabilistic, whereas in the dendrite-based model, all synaptic state changes are deterministic: during learning, weak synapses receiving the instruction to potentiate do so fully and immediately, and during forgetting, strong synapses that reach the end of their lifetimes are fully and immediately depressed.
The logic of synapse durability is also different in the Cascade vs. In the Cascade model, when a synapse is first potentiated, it is in its most labile strong state, and therefore most vulnerable to depression. In the dendrite-based model, a synapse that has just been potentiated is in its most durable state, in the sense that it will withstand the largest number of consecutive learning events in which it does not participate before it "ages out" and finally succumbs to synaptic depression.
In the Benna and Fusi model [ 8 ], the machinery contained within each synapse consists metaphorically of a chain of connected fluid-filled beakers. Synaptic potentiation occurs deterministically, and consists of adding a fixed amount of liquid "weight" to the first beaker; synaptic depression consists of removing that amount of liquid from the first beaker.
The equilibration of liquid levels in the beaker chain following an instructed weight change, and particularly the equilibration of the first beaker, captures the time course of the memory decay at each synapse.
In the example shown in [ 8 ], a synapse consisted of a chain of 12 virtual beakers that doubled in capacity with each step down the chain so that the last beaker had a capacity 2, times that of the first beaker , and whose fluid levels were governed by differential equations with pre-determined rate constants linking each pair of buckets.
As a practical matter, the authors found the number of discrete levels per beaker could be reduced linearly from 35 in the first smallest beaker, corresponding to 35 levels of visible synaptic weight, down to 2 levels in the last largest beaker. Interestingly, unlike the cascade model whose synapses only change state in response to plasticity instructions which can occur asynchronously , the chain-of-beakers model, if taken literally, continues to equilibrate—i.
Thus, an additional layer of mechanism is presumably needed to modulate the inter-beaker flow rates in a coordinated fashion depending on the external learning rate.
In summary, both of these models [ 4 , 8 ] achieve longer memory lifetimes by increasing the complexity of the synapse model as the size of the memory increases. How does a dendrite-based model grow storage capacity without increasing the complexity of the individual synapses?
Within virtually any recognition memory model, the conceptually simplest way to increase storage capacity is to reduce the fraction of synapses that are modified during the storage of each pattern the signal , while correspondingly reducing the response of the memory to random input patterns the noise.
Practically, this can be achieved by sparsifying the input patterns inversely with pattern size as the memory grows larger. Thus, if the memory increases in size from to synapses, in order to increase capacity c-fold, the pattern density 'a' must be reduced c-fold so that the same number of synapses is activated by each pattern as before.
This simple scaling approach runs into the biological plausibility problem that very large capacities require very low pattern densities, and very low depression probabilities. To achieve a capacity of , patterns, for example, only 1 in , input neurons could be active, and synaptic depression would occur in only 1 in , strong synapses.
Reliably controlling such small activity and plasticity probabilities could be difficult to achieve in neural tissue. As an alternative both to this very simple sparsification approach, and to the "complex synapse" approach developed by Fusi and colleagues, adding a layer of dendritic learning units allows the memory to push further into the sparse plasticity regime without the need for very low pattern densities or plasticity probabilities. Relative to a flat 1-layer memory model, dendritic learning thresholds can restrict learning to just a few dendrites from a very large pool.
In our model the formation of new memories is achieved through long-term potentiation or rejuvenation of a few activated synapses on a few strongly activated dendrites that undergo learning events. Given the pressure to keep memory traces at their bare minimum strength, when our model is optimized for capacity, synaptic changes are exceedingly sparse, involving only a small fraction of the synapses on a minute fraction of dendrites. The finding that memory capacity is optimized by sparse patterns has also been reported for 1-layer models: [ 2 , — ].
If we consider extremely sparse synaptic plasticity to be a prediction of our model, could such sparse changes be detected experimentally? The likelihood of detecting changes in this few dendrites seems higher when it is considered that 20, dendrites corresponds to —1, neurons.
We would thus expect that 10 i. In vivo imaging techniques with a field of view containing hundreds of neurons should make this level of detection possible. What role might structural plasticity play in online learning?
We previously explored the role that active dendrites might play in familiarity-based recognition in the very different scenario where patterns can be trained repeatedly [ 46 , ]. The opportunity for repeated, interleaved training of patterns gives the system time to exploit wiring plasticity mechanisms [ ], wherein existing connections between axons and dendrites can be eliminated and new ones formed in such a way that correlated inputs end up forming contacts onto the same dendrites.
This type of wiring plasticity is not an option in an online learning scenario, since each pattern is experienced only once, such that all learning-related synaptic changes must be immediate—or at least immediately induced.
We showed that correlation-based sorting of inputs onto different dendrites using a Hebb-type learning rule increased the storage capacity of a neuron by more than an order of magnitude compared to a neuron with the same total number of synaptic inputs that lacked dendrites.
Furthermore, as here, we found that dendrites of intermediate size optimized capacity—though for different reasons. It is interesting to note that in our current model, structural turnover of weak synapses has no effect on what is stored in the memory, as long as new weak synapses are added to the system at the same rate that existing weak synapses are removed. What would be the advantage of eliminating existing weak connections and forming new ones? Under the assumption that input axons are uncorrelated, as we have assumed in this work for simplicity, we can see no advantage to this type of structural turnover.
However, if meaningful correlations between input axons do exist, then structural turnover could be a sign that wiring plasticity mechanisms are attempting to co-locate correlated synapses on the same dendrites [ , ], which could lead to a significant capacity advantage [ 46 , , ]. Familiarity-based recognition is a very basic form of memory, and is most closely associated with the perirhinal cortex [ 10 , 87 , 88 ]. However, currently available data regarding the responses of familiarity vs.
Further work will be required to determine whether the dendrite-based architecture of Fig 2b will be helpful in explaining familiarity-based recognition processes in the brain. What can the dendrite-based architecture we have studied here tell us about other types of memory systems?
A trivial extension of our architecture in which N copies of the memory network are concatenated would allow the construction of a full N-bit binary online associative memory. This type of memory would behave exactly as ours, but would allow an arbitrary N-bit output pattern to be one-shot associated with each input pattern, as in a Willshaw network.
In this scenario, only the subset of the N networks whose outputs are instructed to be 1 would learn each input pattern, while any networks instructed to produce 0 responses would simply ignore the input pattern. If the output patterns are sparse which they needn't be , only a small fraction of the networks would need to participate in the learning of each association.
It might also be desirable to assign extended lifetimes to particularly important patterns; this could be accomplished in either of two ways: 1 Extended-lifetime synapses could be established during the learning of important patterns, so that the synapses representing those patterns would remain invulnerable to depotentiation for longer times, or even permanently.
Doing so would of course reduce the lifetimes of other patterns in the memory. The decision as to which or how many networks participate in the storage of each pattern could be gated by an "importance" signal provided by another brain area.
In other cases it might be valuable to store different trace strengths for different patterns, rather than uniform, bare-bones recognition traces for all patterns. Note this goal is inconsistent with the goal to maximize storage lifetimes for all patterns, but could also be useful in certain ecological situations. Our simple architecture allows for this directly: nothing is to prevent a larger or small number of dendrites from being used in the learning of any particular pattern, such that it's memory trace would be stronger or weaker than the norm.
The trace strength assigned to each pattern could again be determined by a signal generated by another brain area, whose effect is to raise or lower dendritic learning thresholds. In yet another scenario it might be useful to store gradually decaying memory traces so that trace strength can represent recency of learning which is again a different goal than maximizing recognition capacity. Early in its storage lifetime, the pattern would evoke a memory trace from all networks, so that it's total trace strength would be high, but as time progresses, and its trace progressively expires from the lower-capacity networks, its overall trace strength would gradually decay.
This use of such a tiered system to achieve a graded decay time course is more resource-efficient than certain other forms of trace decay that have been considered in the online memory literature, in that the stored information in a tiered network with synapse age management expires in a controlled fashion [ ].
Finally, it will require future work to determine which of our results can carry over to Hopfield-style recurrent networks [ — ] constructed from neurons with thresholded dendrites, where the goal in that case would be to maximize recall capacity.
In one obvious difference, the ability to recall entire patterns from partial cues requires that the entire patterns be stored in stark contrast to the need to generate only a reliable familiarity signal , so synapse resource consumption per pattern will be much higher than in the basic familiarity network. Furthermore, the need to modify recurrent synapses during the initial learning of a pattern implies that the participating neurons must fire action potentials during initial learning in order to activate those recurrent connections, which implies that their dendrites must cross both the learning and firing thresholds during learning.
This incompatibility could be one reason why the functions of familiarity and recall memory have been assigned to distinct areas within the medial temporal lobe [ 87 , 88 ].
We refer to the number of learning events that can be endured before this loss occurs as the length of the age queue L. Consider a single synapse on a given dendrite. If is the vector containing the probability that, at a given time, this synapse is in each of the states shown in Fig 3 , and is the matrix containing the state transition probabilities, then with each learning event, will change as.
After many learning events, will approach the equilibrium distribution, characterized by the condition that learning leaves it unchanged:. Using the fact that for the equilibrium distribution of the synapses must be strong, one can solve for since the vector implicitly depends on. Using the eigenvectors and eigenvalues of , one can also compute the distribution after any number of learning events.
However, while the Markov approach is very general, the simple dynamics of the age queue allow for a more direct and transparent derivation of. To find , we might naively divide the total number of strong synapses per dendrite by the average number of synapses potentiated in each dendrite that experiences a learning event. In words, is approximately equal to the total number of spikes impinging on all activated synapses on the dendrite, given by the threshold value since in most cases learning dendrites will have just crossed this threshold , divided by the average number of spikes per participating synapse.
This gives. However, this would underestimate L because synapses that are only juvenated i. To estimate more accurately, consider the equilibrium distribution of synapse ages in the queue of a single dendrite blue histogram in Fig 3. The age of the right-most column of the age histogram is an indicator of the expected age measured in learning events at which the synapses encoding a pattern are depressed and moved to the unordered collection of weak synapses.
During each learning event, a large fraction of synapses in each column that were not activated move rightward to the next older column, while a small fraction are juvenated promoted to the first column. This process leads to a bias towards younger synapses in the queue, and can be well-approximated by a finite geometric sequence with length , decay ratio , sum note the sum of the columns is the total number of strong synapses , and first column height the average number of synapses that learn per dendrite per learning event , so that:.
Assuming that the synapses in a dendrite are all equally likely to be potentiated ignoring the effects of the postsynaptic threshold—see below , with , then we have that and can solve the above equation for.
Note that counts the number of dendritic learning events before a memory is eroded, whereas memory capacity C should count the number of training patterns. Although is conceptually simple, its expression is complicated since it depends on pattern density, noise level, two learning thresholds, dendrite size, and see expression below. Collecting these results, we can approximate memory capacity by. For simplicity, the expression for in the capacity equation does not include the effect of the postsynaptic threshold , which makes strong synapses more likely to learn, lowers and increases absolute capacity.
The synapse age distribution remains roughly geometric, however see Fig 5b , and we observed that the qualitative behavior of the system depends only weakly on , justifying its omission from the analysis. Synaptic activation on a dendrite is governed by 4 binomial random variables: , the number of active strong synapses; , the number of spikes received by strong synapses; , the number of active weak synapses; and , the number of spikes received by weak synapses. These random variables have the distributions shown below.
Learning occurs when presynaptic activation crosses the presynaptic learning threshold, or , and postsynaptic activation crosses the postsynaptic learning threshold, or Using the distributions for and , and the fact that we can write an explicit expression for : where is the binomial pdf with parameters evaluated at. A simpler alternative to evaluating this expression directly is to estimate it by generating a large number of samples of and according to the above distributions, and directly observing the fraction of cases that cross both learning thresholds.
Once the capacity formula is used to calculate how long a given memory trace will last, we must verify that during its lifetime, the trace is sufficiently strong. We do this by checking whether the error tolerances and are met immediately after training. First, we compute , the probability that an untrained pattern will be recognized.
To be recognized, a pattern must activate at least dendrites in the network. For a randomly selected untrained pattern, the distribution of the number of activated dendrites will be approximately Poisson with mean , where is the number of dendrites in the network and is the probability that a given dendrite fires in response to a randomly selected pattern.
For a pattern to fire a dendrite, it must cause a postsynaptic activation , or , using the notation of above. To calculate , we use the following observation: when training a new pattern, it will learn in a certain set of dendrites. In other words, dendrite readout failures immediately after learning should be very rare. Therefore, for a pattern to be too weak for recognition immediately after training, it must have learned in too few dendrites.
The number of learning dendrites for a given pattern will have a Poisson distribution with mean. Therefore, can be written If for the given settings of the learning and firing thresholds , the error tolerances are met—that is, then the memory lifetime is compared to the best memory lifetime found so far.
Otherwise, we continue the search through threshold space. In the base case without background noise, nominally inactive axons which were the vast majority never fired. For the medium and high noise cases, nominally inactive axons emitted one spike with the indicated probability. Increasing background noise decreased memory capacity, and, at high noise levels, pushed the optimal dendrite size to shorter values.
For all simulations here, the dendritic activation slope parameter was set to 3. We then tested how a trained network responded to perturbed versions of stored patterns. As expected, as an increasing fraction of training pattern bits were changed, network response decreased black curve. We then tested whether the network could reliably distinguish between exact trained patterns and perturbed patterns red curve.
Abstract In order to record the stream of autobiographical information that defines our unique personal history, our brains must form durable memories from single brief exposures to the patterned stimuli that impinge on them continuously throughout life.
Author summary Humans can effortlessly recognize a pattern as familiar even after a single presentation and a long delay, and our capacity to do so even with complex stimuli such as images has been called "almost limitless". Introduction To function well in a complex world, our brains must somehow stream our everyday experiences into memory as they occur in real time.
Download: PPT. Fig 1. Online learning in a familiarity-based recognition memory. Table 1. List of parameter categories, and specific parameters, used in the analysis and simulations.
Results We modeled the memory network depicted in Fig 2a , consisting of a set of axons that form sparse random connections with the dendrites of a population of target neurons. The network The network structure and plasticity rules have been previously described in [ 7 ], but are repeated here for clarity. The synaptic learning rule The goal of learning is to ensure that learned patterns going back as far as possible in time produce suprathreshold network responses , while randomly drawn patterns do not.
Calculating memory capacity One of the key quantities involved in calculating storage capacity is , the length of the age queue within a dendrite see Fig 3.
Determining optimal dendrite size How can the expression for online storage capacity Eq 2 be exploited? Fig 5. Validating the analytical model with full network simulations. Bergmann glia responsible for migration By 18 weeks gestation, all cortical neurons have reached designated location Migratory defects include complete failure of migration; curtailment of migratory cells along migratory pathway; aberrant placement of postmitotic neurons within target structure ectopia Aggregation — during migratory cycles, neurons selectively aggregate to form cellular masses, or layers.
This is called lamination. Extensions spines begin to extend from dendrites Dendritic growth begins prenatally and proceeds slowly Majority of arborization and spine growth occurs postnatally, with most intensive period occurring birth to 18 months Development highly sensitive to environmental stimulation Chemospecificity — biochemical specificity programmed into each nerve cell determining that contacts between cells are made. As neuron forms axon and dendrites, sends out advance spray of cellular processes microfilaments that seek chemical attraction, forming appropriate connections with nerve cells.
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