6,068 research outputs found
Learning and generation of long-range correlated sequences
We study the capability to learn and to generate long-range, power-law
correlated sequences by a fully connected asymmetric network. The focus is set
on the ability of neural networks to extract statistical features from a
sequence. We demonstrate that the average power-law behavior is learnable,
namely, the sequence generated by the trained network obeys the same
statistical behavior. The interplay between a correlated weight matrix and the
sequence generated by such a network is explored. A weight matrix with a
power-law correlation function along the vertical direction, gives rise to a
sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review
Secure and linear cryptosystems using error-correcting codes
A public-key cryptosystem, digital signature and authentication procedures
based on a Gallager-type parity-check error-correcting code are presented. The
complexity of the encryption and the decryption processes scale linearly with
the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted
by Bob, whereas a private-noise added by Alice to a given fraction of the
ciphertext of each encrypted plaintext serves to increase the secure channel
and is the cornerstone for digital signatures and authentication. Various
scenarios are discussed including the possible actions of the opponent Oscar as
an eavesdropper or as a disruptor
Secure exchange of information by synchronization of neural networks
A connection between the theory of neural networks and cryptography is
presented. A new phenomenon, namely synchronization of neural networks is
leading to a new method of exchange of secret messages. Numerical simulations
show that two artificial networks being trained by Hebbian learning rule on
their mutual outputs develop an antiparallel state of their synaptic weights.
The synchronized weights are used to construct an ephemeral key exchange
protocol for a secure transmission of secret data. It is shown that an opponent
who knows the protocol and all details of any transmission of the data has no
chance to decrypt the secret message, since tracking the weights is a hard
problem compared to synchronization. The complexity of the generation of the
secure channel is linear with the size of the network.Comment: 11 pages, 5 figure
Learning and predicting time series by neural networks
Artificial neural networks which are trained on a time series are supposed to
achieve two abilities: firstly to predict the series many time steps ahead and
secondly to learn the rule which has produced the series. It is shown that
prediction and learning are not necessarily related to each other. Chaotic
sequences can be learned but not predicted while quasiperiodic sequences can be
well predicted but not learned.Comment: 5 page
Generation of unpredictable time series by a Neural Network
A perceptron that learns the opposite of its own output is used to generate a
time series. We analyse properties of the weight vector and the generated
sequence, like the cycle length and the probability distribution of generated
sequences. A remarkable suppression of the autocorrelation function is
explained, and connections to the Bernasconi model are discussed. If a
continuous transfer function is used, the system displays chaotic and
intermittent behaviour, with the product of the learning rate and amplification
as a control parameter.Comment: 11 pages, 14 figures; slightly expanded and clarified, mistakes
corrected; accepted for publication in PR
Training a perceptron by a bit sequence: Storage capacity
A perceptron is trained by a random bit sequence. In comparison to the
corresponding classification problem, the storage capacity decreases to
alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The
numerical results are supported by a signal to noise analysis of Hebbian
weights.Comment: LaTeX, 13 pages incl. 4 figures and 1 tabl
Do rBST-Free and Organic Milk Stigmatize Conventionally Produced Milk?
Producers are continually seeking to differentiate their products in the marketplace. A common approach is via labeling where differences in production methods are marketed. Yet, positive labeling for the new product has the potential to stigmatize the conventionally produced product by highlighting perceived problems with the product. The net economic result can be negative to producers as the conventional product that dominates the market is stigmatized by the new product that has little market share, and this leads to consumers decreasing their willingness to pay for the conventional product. This experimental research identifies this stigma effect in the case of milk, where the presentation of rBST-Free milk reduces consumers' willingness to purchase conventional milk.Demand and Price Analysis,
Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
We present the interplay between synchronization of unidirectional coupled
chaotic nodes with heterogeneous delays and the greatest common divisor (GCD)
of loops composing the oriented graph. In the weak chaos region and for GCD=1
the network is in chaotic zero-lag synchronization, whereas for GCD=m>1
synchronization of m-sublattices emerges. Complete synchronization can be
achieved when all chaotic nodes are influenced by an identical set of delays
and in particular for the limiting case of homogeneous delays. Results are
supported by simulations of chaotic systems, self-consistent and mixing
arguments, as well as analytical solutions of Bernoulli maps.Comment: 7 pages, 5 figure
Genetic attack on neural cryptography
Different scaling properties for the complexity of bidirectional
synchronization and unidirectional learning are essential for the security of
neural cryptography. Incrementing the synaptic depth of the networks increases
the synchronization time only polynomially, but the success of the geometric
attack is reduced exponentially and it clearly fails in the limit of infinite
synaptic depth. This method is improved by adding a genetic algorithm, which
selects the fittest neural networks. The probability of a successful genetic
attack is calculated for different model parameters using numerical
simulations. The results show that scaling laws observed in the case of other
attacks hold for the improved algorithm, too. The number of networks needed for
an effective attack grows exponentially with increasing synaptic depth. In
addition, finite-size effects caused by Hebbian and anti-Hebbian learning are
analyzed. These learning rules converge to the random walk rule if the synaptic
depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
A Changing Public Policy: Garnishment of Municipal Corporations in Illinois - Henderson v. Foster
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