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

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

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

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

Analysis of Oscillator Neural Networks for Sparsely Coded Phase Patterns

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical neurodynamics to our model, we theoretically investigate the model's associative memory capability by evaluating its maximum storage capacities and deriving its basins of attraction. It is shown that, as in the Hopfield model, the storage capacity diverges as the activity level decreases. We consider various practically and theoretically important cases. For example, it is revealed that a dynamically adjusted threshold mechanism enhances the retrieval ability of the associative memory. It is also found that, under suitable conditions, the network can recall patterns even in the case that patterns with different activity levels are stored at the same time. In addition, we examine the robustness with respect to damage of the synaptic connections. The validity of these theoretical results is confirmed by reasonable agreement with numerical simulations.Comment: 23 pages, 11 figure

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

Nonspecific synaptic plasticity improves the recognition of sparse patterns degraded by local noise

Safaryan, K. et al. Nonspecific synaptic plasticity improves the recognition of sparse patterns degraded by local noise. Sci. Rep. 7, 46550; doi: 10.1038/srep46550 (2017). This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ © The Author(s) 2017.Many forms of synaptic plasticity require the local production of volatile or rapidly diffusing substances such as nitric oxide. The nonspecific plasticity these neuromodulators may induce at neighboring non-active synapses is thought to be detrimental for the specificity of memory storage. We show here that memory retrieval may benefit from this non-specific plasticity when the applied sparse binary input patterns are degraded by local noise. Simulations of a biophysically realistic model of a cerebellar Purkinje cell in a pattern recognition task show that, in the absence of noise, leakage of plasticity to adjacent synapses degrades the recognition of sparse static patterns. However, above a local noise level of 20 %, the model with nonspecific plasticity outperforms the standard, specific model. The gain in performance is greatest when the spatial distribution of noise in the input matches the range of diffusion-induced plasticity. Hence non-specific plasticity may offer a benefit in noisy environments or when the pressure to generalize is strong.Peer reviewe

An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $\alpha_c = P_{\rm max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This storage capacity of our temporal-code network is comparable to that of the rate-code model with the Willshaw-type synapses. Our HH neuron network is realized not to be vulnerable to the distribution of time delays in couplings. The variability of interspace interval (ISI) of output spike trains in the process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl