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

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

Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value

We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge $Z\alpha=2/\pi$.Comment: LaTeX2e, 12 page

Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure

The Konkoly Blazhko Survey: Is light-curve modulation a common property of RRab stars?

A systematic survey to establish the true incidence rate of the Blazhko modulation among short-period, fundamental-mode, Galactic field RR Lyrae stars has been accomplished. The Konkoly Blazhko Survey (KBS) was initiated in 2004. Since then more than 750 nights of observation have been devoted to this project. A sample of 30 RRab stars was extensively observed, and light-curve modulation was detected in 14 cases. The 47% occurrence rate of the modulation is much larger than any previous estimate. The significant increase of the detected incidence rate is mostly due to the discovery of small-amplitude modulation. Half of the Blazhko variables in our sample show modulation with so small amplitude that definitely have been missed in the previous surveys. We have found that the modulation can be very unstable in some cases, e.g. RY Com showed regular modulation only during one part of the observations while during two seasons it had stable light curve with abrupt, small changes in the pulsation amplitude. This type of light-curve variability is also hard to detect in other Survey's data. The larger frequency of the light-curve modulation of RRab stars makes it even more important to find the still lacking explanation of the Blazhko phenomenon. The validity of the [Fe/H](P,phi_{31}) relation using the mean light curves of Blazhko variables is checked in our sample. We have found that the formula gives accurate result for small-modulation-amplitude Blazhko stars, and this is also the case for large-modulation-amplitude stars if the light curve has complete phase coverage. However, if the data of large-modulation-amplitude Blazhko stars are not extended enough (e.g. < 500 data points from < 15 nights), the formula may give false result due to the distorted shape of the mean light curve used.Comment: Accepted for publication in MNRAS, 14 pages, 7 Figure

Multi-Choice Minority Game

The generalization of the problem of adaptive competition, known as the minority game, to the case of $K$ possible choices for each player is addressed, and applied to a system of interacting perceptrons with input and output units of the type of $K$-states Potts-spins. An optimal solution of this minority game as well as the dynamic evolution of the adaptive strategies of the players are solved analytically for a general $K$ and compared with numerical simulations.Comment: 5 pages, 2 figures, reorganized and clarifie

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

Estimating specific surface area of fine stream bed sediments from geochemistry

Specific surface area (SSA) of headwater stream bed sediments is a fundamental property which determines the nature of sediment surface reactions and influences ecosystem-level, biological processes. Measurements of SSA – commonly undertaken by BET nitrogen adsorption – are relatively costly in terms of instrumentation and operator time. A novel approach is presented for estimating fine (2.5 mg kg−1), four elements were identified as significant predictors of SSA (ordered by decreasing predictive power): V > Ca > Al > Rb. The optimum model from these four elements accounted for 73% of the variation in bed sediment SSA (range 6–46 m2 g−1) with a root mean squared error of prediction – based on leave-one-out cross-validation – of 6.3 m2 g−1. It is believed that V is the most significant predictor because its concentration is strongly correlated both with the quantity of Fe-oxides and clay minerals in the stream bed sediments, which dominate sediment SSA. Sample heterogeneity in SSA – based on triplicate measurements of sub-samples – was a substantial source of variation (standard error = 2.2 m2 g−1) which cannot be accounted for in the regression model. The model was used to estimate bed sediment SSA at the other 1792 sites and at 30 duplicate sites where an extra sediment sample had been collected, 25 m from the original site. By delineating sub-catchments for the headwater sediment sites only those sub-catchments were selected with a dominant (>50% of the sub-catchment area) bedrock formation and land use type; the bedrock and land use classes accounted for 39% and 7% of the variation in bed sediment SSA, respectively. Variation in estimated, fine bed sediment SSA from the paired, duplicate sediment sites was small (2.7 m2 g−1), showing that local variation in SSA at stream sites is modest when compared to that between catchments. How the approach might be applied in other environments and its potential limitations are discussed

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

The influence of feature selection methods on accuracy, stability and interpretability of molecular signatures

Motivation: Biomarker discovery from high-dimensional data is a crucial problem with enormous applications in biology and medicine. It is also extremely challenging from a statistical viewpoint, but surprisingly few studies have investigated the relative strengths and weaknesses of the plethora of existing feature selection methods. Methods: We compare 32 feature selection methods on 4 public gene expression datasets for breast cancer prognosis, in terms of predictive performance, stability and functional interpretability of the signatures they produce. Results: We observe that the feature selection method has a significant influence on the accuracy, stability and interpretability of signatures. Simple filter methods generally outperform more complex embedded or wrapper methods, and ensemble feature selection has generally no positive effect. Overall a simple Student's t-test seems to provide the best results. Availability: Code and data are publicly available at http://cbio.ensmp.fr/~ahaury/