The Hamilton-Jacobi analysis for higher-order modified gravity

The Hamilton-Jacobi $[HJ]$ study for the Chern-Simons $[CS]$ modification of general relativity $[GR]$ is performed. The complete structure of the Hamiltonians and the generalized brackets are reported, from these results the $HJ$ fundamental differential is constructed and the symmetries of the theory are found. By using the Hamiltonians we remove an apparent Ostrogradsky's instability and the new structure of the hamiltonian is reported. In addition, the counting of physical degrees of freedom is developed and some remarks are discussed

Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays

We propose that systems exhibiting compositional patterning at the nanoscale, so far assumed to be due to some kind of ordered phase segregation, can be understood instead in terms of coherent, single phase ordering of minority motifs, caused by some constrained drive for uniformity. The essential features of this type of arrangements can be reproduced using a superspace construction typical of uniformity-driven orderings, which only requires the knowledge of the modulation vectors observed in the diffraction patterns. The idea is discussed in terms of a simple two dimensional lattice-gas model that simulates a binary system in which the dilution of the minority component is favored. This simple model already exhibits a hierarchy of arrangements similar to the experimentally observed nano-chessboard and nano-diamond patterns, which are described as occupational modulated structures with two independent modulation wave vectors and simple step-like occupation modulation functions.Comment: Preprint. 11 pages, 11 figure

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks

The nature of dark matter and the density profile and central behavior of relaxed halos

We show that the two basic assumptions of the model recently proposed by Manrique and coworkers for the universal density profile of cold dark matter (CDM) halos, namely that these objects grow inside out in periods of smooth accretion and that their mass profile and its radial derivatives are all continuous functions, are both well understood in terms of the very nature of CDM. Those two assumptions allow one to derive the typical density profile of halos of a given mass from the accretion rate characteristic of the particular cosmology. This profile was shown by Manrique and coworkers to recover the results of numerical simulations. In the present paper, we investigate its behavior beyond the ranges covered by present-day N-body simulations. We find that the central asymptotic logarithmic slope depends crucially on the shape of the power spectrum of density perturbations: it is equal to a constant negative value for power-law spectra and has central cores for the standard CDM power spectrum. The predicted density profile in the CDM case is well fitted by the 3D S\'ersic profile over at least 10 decades in halo mass. The values of the S\'ersic parameters depend on the mass of the structure considered. A practical procedure is provided that allows one to infer the typical values of the best NFW or S\'ersic fitting law parameters for halos of any mass and redshift in any given standard CDM cosmology.Comment: 9 pages, 6 figures, to appear in the ApJ vol. 647, september 20, 2007. Minor changes to match the published versio

The Effects of the Peak-Peak Correlation on the Peak Model of Hierarchical Clustering

In two previous papers a semi-analytical model was presented for the hierarchical clustering of halos via gravitational instability from peaks in a random Gaussian field of density fluctuations. This model is better founded than the extended Press-Schechter model, which is known to agree with numerical simulations and to make similar predictions. The specific merger rate, however, shows a significant departure at intermediate captured masses. The origin of this was suspected as being the rather crude approximation used for the density of nested peaks. Here, we seek to verify this suspicion by implementing a more accurate expression for the latter quantity which accounts for the correlation among peaks. We confirm that the inclusion of the peak-peak correlation improves the specific merger rate, while the good behavior of the remaining quantities is preserved.Comment: ApJ accepted. 15 pages, including 4 figures. Also available at ftp://pcess1.am.ub.es/pub/ApJ/effectpp.ps.g

Alliance free and alliance cover sets

A \emph{defensive} (\emph{offensive}) $k$-\emph{alliance} in $\Gamma=(V,E)$ is a set $S\subseteq V$ such that every $v$ in $S$ (in the boundary of $S$) has at least $k$ more neighbors in $S$ than it has in $V\setminus S$. A set $X\subseteq V$ is \emph{defensive} (\emph{offensive}) $k$-\emph{alliance free,} if for all defensive (offensive) $k$-alliance $S$, $S\setminus X\neq\emptyset$, i.e., $X$ does not contain any defensive (offensive) $k$-alliance as a subset. A set $Y \subseteq V$ is a \emph{defensive} (\emph{offensive}) $k$-\emph{alliance cover}, if for all defensive (offensive) $k$-alliance $S$, $S\cap Y\neq\emptyset$, i.e., $Y$ contains at least one vertex from each defensive (offensive) $k$-alliance of $\Gamma$. In this paper we show several mathematical properties of defensive (offensive) $k$-alliance free sets and defensive (offensive) $k$-alliance cover sets, including tight bounds on the cardinality of defensive (offensive) $k$-alliance free (cover) sets

Noise-tolerant Modular Neural Network System for Classifying ECG Signal

Millions of electrocardiograms (ECG) are interpreted every year, requiring specialized training for accurate interpretation. Because automated and accurate classification ECG signals will improve early diagnosis of heart condition, several neural network (NN) approaches have been proposed for classifying ECG signals. Current strategies for a critical step, the preprocessing for noise removal, are still unsatisfactory. We propose a modular NN approach based on artificial noise injection, to improve the generalization capability of the resulting model. The NN classifier initially performed a fairly accurate recognition of four types of cardiac anomalies in simulated ECG signals with minor, moderate, severe, and extreme noise, with an average accuracy of 99.2%, 95.1%, 91.4%, and 85.2% respectively. Ultimately we discriminated normal and abnormal heartbeat patterns for single lead of raw ECG signals, obtained 95.7% of overall accuracy and 99.5% of Precision. Therefore, the propose approach is a useful tool for the detection and diagnosis of cardiac abnormalities