50 research outputs found
Cross-correlation dynamics in financial time series
The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of
the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined. A basic one-factor model is proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a market plus sectors model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found
for empirical data
Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
Recently we introduced a family of invariant Random Matrix Ensembles
which is characterized by a parameter describing logarithmic
soft-confinement potentials ). We
showed that we can study eigenvalue correlations of these "-ensembles"
based on the numerical construction of the corresponding orthogonal polynomials
with respect to the weight function . In this
work, we expand our previous work and show that: i) the eigenvalue density is
given by a power-law of the form and
ii) the two-level kernel has an anomalous structure, which is characteristic of
the critical ensembles. We further show that the anomalous part, or the
so-called "ghost-correlation peak", is controlled by the parameter ;
decreasing increases the anomaly. We also identify the two-level
kernel of the -ensembles in the semiclassical regime, which can be
written in a sinh-kernel form with more general argument that reduces to that
of the critical ensembles for . Finally, we discuss the universality
of the -ensembles, which includes Wigner-Dyson universality ( limit), the uncorrelated Poisson-like behavior (
limit), and a critical behavior for all the intermediate
() in the semiclassical regime. We also comment on the
implications of our results in the context of the localization-delocalization
problems as well as the dependence of the two-level kernel of the fat-tail
random matrices.Comment: 10 pages, 13 figure
Seizure characterisation using frequency-dependent multivariate dynamics
The characterisation of epileptic seizures assists in the design of targeted pharmaceutical seizure prevention techniques
and pre-surgical evaluations. In this paper, we expand on recent use of multivariate techniques to study the crosscorrelation
dynamics between electroencephalographic (EEG) channels. The Maximum Overlap Discrete Wavelet
Transform (MODWT) is applied in order to separate the EEG channels into their underlying frequencies. The
dynamics of the cross-correlation matrix between channels, at each frequency, are then analysed in terms of the
eigenspectrum. By examination of the eigenspectrum, we show that it is possible to identify frequency dependent
changes in the correlation structure between channels which may be indicative of seizure activity.
The technique is applied to EEG epileptiform data and the results indicate that the correlation dynamics vary over
time and frequency, with larger correlations between channels at high frequencies. Additionally, a redistribution of wavelet energy is found, with increased fractional energy demonstrating the relative importance of high frequencies
during seizures. Dynamical changes also occur in both correlation and energy at lower frequencies during seizures,
suggesting that monitoring frequency dependent correlation structure can characterise changes in EEG signals during
these. Future work will involve the study of other large eigenvalues and inter-frequency correlations to determine
additional seizure characteristics
Amenability of algebras of approximable operators
We give a necessary and sufficient condition for amenability of the Banach
algebra of approximable operators on a Banach space. We further investigate the
relationship between amenability of this algebra and factorization of
operators, strengthening known results and developing new techniques to
determine whether or not a given Banach space carries an amenable algebra of
approximable operators. Using these techniques, we are able to show, among
other things, the non-amenability of the algebra of approximable operators on
Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic
Laser ablation loading of a radiofrequency ion trap
The production of ions via laser ablation for the loading of radiofrequency
(RF) ion traps is investigated using a nitrogen laser with a maximum pulse
energy of 0.17 mJ and a peak intensity of about 250 MW/cm^2. A time-of-flight
mass spectrometer is used to measure the ion yield and the distribution of the
charge states. Singly charged ions of elements that are presently considered
for the use in optical clocks or quantum logic applications could be produced
from metallic samples at a rate of the order of magnitude 10^5 ions per pulse.
A linear Paul trap was loaded with Th+ ions produced by laser ablation. An
overall ion production and trapping efficiency of 10^-7 to 10^-6 was attained.
For ions injected individually, a dependence of the capture probability on the
phase of the RF field has been predicted. In the experiment this was not
observed, presumably because of collective effects within the ablation plume.Comment: submitted to Appl. Phys. B., special issue on ion trappin
Coherent States Measurement Entropy
Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail:
[email protected]). Submitted to J.Phys.
Influence of the Time Scale on the Construction of Financial Networks
BACKGROUND: In this paper we investigate the definition and formation of financial networks. Specifically, we study the influence of the time scale on their construction. METHODOLOGY/PRINCIPAL FINDINGS: For our analysis we use correlation-based networks obtained from the daily closing prices of stock market data. More precisely, we use the stocks that currently comprise the Dow Jones Industrial Average (DJIA) and estimate financial networks where nodes correspond to stocks and edges correspond to none vanishing correlation coefficients. That means only if a correlation coefficient is statistically significant different from zero, we include an edge in the network. This construction procedure results in unweighted, undirected networks. By separating the time series of stock prices in non-overlapping intervals, we obtain one network per interval. The length of these intervals corresponds to the time scale of the data, whose influence on the construction of the networks will be studied in this paper. CONCLUSIONS/SIGNIFICANCE: Numerical analysis of four different measures in dependence on the time scale for the construction of networks allows us to gain insights about the intrinsic time scale of the stock market with respect to a meaningful graph-theoretical analysis
Écfrasis de ida y vuelta: monólogo dramático y culturalismo en «Trébol», de Rubén Darío
De los numerosos homenajes que Rubén Darío compuso a lo largo de su trayectoria poética, uno de los que más subversivamente ha sido tratado por la crítica es «Trébol», palabra en la que aparecen agrupados tres sonetos donde el poeta nicaragüense realizó su particular veneración a las figuras de Velázquez y Góngora. En este trabajo se lleva a cabo un estudio sobre la técnica y el procedimiento de composición poética utilizada en estos textos, así como su análisis estilístico, para finalizar con el replanteamiento de una cuestión polémica: el posible gongorismo de Rubén Darío en dichos sonetos.From the abundant tributes that Rubén Darío wrote during his poetic career, one of the most subversively treated by Dario’s critics is the one named «Trébol», a word in which three sonnets are showed grouped together where the Nicaraguan poet paid his particular tribute to Velázquez and Góngora. In this article, a study on the technique and poetic composition of these texts is fulfilled, as well as a stylistic analysis of them, to conclude with a rethinking of a controversial issue: the potential gongorism of Rubén Darío in these sonnets