290 research outputs found
Synergetic Analysis of the Haeussler-von der Malsburg Equations for Manifolds of Arbitrary Geometry
We generalize a model of Haeussler and von der Malsburg which describes the
self-organized generation of retinotopic projections between two
one-dimensional discrete cell arrays on the basis of cooperative and
competitive interactions of the individual synaptic contacts. Our generalized
model is independent of the special geometry of the cell arrays and describes
the temporal evolution of the connection weights between cells on different
manifolds. By linearizing the equations of evolution around the stationary
uniform state we determine the critical global growth rate for synapses onto
the tectum where an instability arises. Within a nonlinear analysis we use then
the methods of synergetics to adiabatically eliminate the stable modes near the
instability. The resulting order parameter equations describe the emergence of
retinotopic projections from initially undifferentiated mappings independent of
dimension and geometry.Comment: Dedicated to Hermann Haken on the occasion of his 80th birthda
Elastic net model of ocular dominance - overall stripe pattern and monocular deprivation
The elastic net (Durbin and Willshaw 1987) can account for the development of both topography and ocular dominance in the mapping from the lateral geniculate nucleus to primary visual cortex (Goodhill and Willshaw 1990). Here it is further shown for this model that (1) the overall pattern of stripes produced is strongly influenced by the shape of the cortex: in particular, stripes with a global order similar to that seen biologically can be produced under appropriate conditions, and (2) the observed changes in stripe width associated with monocular deprivation are reproduced in the model
Large Developing Axonal Arbors Using a Distributed and Locally-Reprogrammable Address-Event Receiver
Thresholds in layered neural networks with variable activity
The inclusion of a threshold in the dynamics of layered neural networks with
variable activity is studied at arbitrary temperature. In particular, the
effects on the retrieval quality of a self-controlled threshold obtained by
forcing the neural activity to stay equal to the activity of the stored paterns
during the whole retrieval process, are compared with those of a threshold
chosen externally for every loading and every temperature through optimisation
of the mutual information content of the network. Numerical results, mostly
concerning low activity networks are discussed.Comment: 15 pages, Latex2e, 6 eps figure
Naturally Rehearsing Passwords
We introduce quantitative usability and security models to guide the design
of password management schemes --- systematic strategies to help users create
and remember multiple passwords. In the same way that security proofs in
cryptography are based on complexity-theoretic assumptions (e.g., hardness of
factoring and discrete logarithm), we quantify usability by introducing
usability assumptions. In particular, password management relies on assumptions
about human memory, e.g., that a user who follows a particular rehearsal
schedule will successfully maintain the corresponding memory. These assumptions
are informed by research in cognitive science and validated through empirical
studies. Given rehearsal requirements and a user's visitation schedule for each
account, we use the total number of extra rehearsals that the user would have
to do to remember all of his passwords as a measure of the usability of the
password scheme. Our usability model leads us to a key observation: password
reuse benefits users not only by reducing the number of passwords that the user
has to memorize, but more importantly by increasing the natural rehearsal rate
for each password. We also present a security model which accounts for the
complexity of password management with multiple accounts and associated
threats, including online, offline, and plaintext password leak attacks.
Observing that current password management schemes are either insecure or
unusable, we present Shared Cues--- a new scheme in which the underlying secret
is strategically shared across accounts to ensure that most rehearsal
requirements are satisfied naturally while simultaneously providing strong
security. The construction uses the Chinese Remainder Theorem to achieve these
competing goals
On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model
During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer's (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer's (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer's (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer
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