Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE

The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, $\mathbf{C}$, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.Comment: 15 pages, 8 figures, to appear in Proceedings of International Workshop on "Econophysics & Sociophysics of Markets & Networks" (Econophys-Kolkata III), Mar 12-15, 200

U.S. stock market interaction network as learned by the Boltzmann Machine

We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented analysis shows that binarization preserves market correlation structure. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We found that a heavy positive tail in the distribution of couplings is responsible for the sparse market clustering structure. We also show that discrepancies between the model parameters might be used as a precursor of financial instabilities.Comment: 15 pages, 17 figures, 1 tabl

Mice with cleavage-resistant N-cadherin exhibit synapse anomaly in the hippocampus and outperformance in spatial learning tasks

N-cadherin is a homophilic cell adhesion molecule that stabilizes excitatory synapses, by connecting pre- and post-synaptic termini. Upon NMDA receptor (NMDAR) activation by glutamate, membrane-proximal domains of N-cadherin are cleaved serially by a-disintegrin-and-metalloprotease 10 (ADAM10) and then presenilin 1(PS1, catalytic subunit of the γ-secretase complex). To assess the physiological significance of the initial N-cadherin cleavage, we engineer the mouse genome to create a knock-in allele with tandem missense mutations in the mouse N-cadherin/Cadherin-2 gene (Cdh2 R714G, I715D, or GD) that confers resistance on proteolysis by ADAM10 (GD mice). GD mice showed a better performance in the radial maze test, with significantly less revisiting errors after intervals of 30 and 300 s than WT, and a tendency for enhanced freezing in fear conditioning. Interestingly, GD mice reveal higher complexity in the tufts of thorny excrescence in the CA3 region of the hippocampus. Fine morphometry with serial section transmission electron microscopy (ssTEM) and three-dimensional (3D) reconstruction reveals significantly higher synaptic density, significantly smaller PSD area, and normal dendritic spine volume in GD mice. This knock-in mouse has provided in vivo evidence that ADAM10-mediated cleavage is a critical step in N-cadherin shedding and degradation and involved in the structure and function of glutamatergic synapses, which affect the memory function

Detection of Multi-TeV Gamma Rays from Markarian 501 during an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array

In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest source in the sky at TeV energies, showing strong and frequent flaring. Using the data obtained with a high density air shower array that has been operating successfully at Yangbajing in Tibet since 1996, we searched for gamma-ray signals from this source during the period from February through August in 1997. Our observation detected multi-TeV $\gamma$-ray signals at the 3.7-Sigma level during this period. The most rapid increase of the excess counts was observed between April 7 and June 16 and the statistical significance of the excess counts in this period was 4.7-Sigma. Among several observations of flaring TeV gamma-rays from Mrk 501 in 1997, this is the only observation using a conventional air shower array. We present the energy spectrum of gamma-rays which will be worthy to compare with those obtained by imaging atmospheric Cerenkov telescopes.Comment: 9 pages, 7 figures, To appear in Ap

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Observation of Multi-Tev Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array

The Tibet experiment, operating at Yangbajing (4,300 m above sea level), is the lowest energy air shower array and the new high density array constructed in 1996 has sensitivity to $\gamma$-ray air showers at energies as low as 3 TeV. With this new array, the Crab Nebula was observed in multi-TeV $\gamma$-rays and a signal was detected at the 5.5 $\sigma$ level. We also obtained the energy spectrum of $\gamma$-rays in the energy region above 3 TeV which partially overlaps those observed with imaging atmospheric Cherenkov telescopes. This is the first observation of $\gamma$-ray signals from point sources with a conventional air shower array using scintillation detectors.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter

Primary proton spectrum between 200 TeV and 1000 TeV observed with the Tibet burst detector and air shower array

Since 1996, a hybrid experiment consisting of the emulsion chamber and burst detector array and the Tibet-II air-shower array has been operated at Yangbajing (4300 m above sea level, 606 g/cm^2) in Tibet. This experiment can detect air-shower cores, called as burst events, accompanied by air showers in excess of about 100 TeV. We observed about 4300 burst events accompanied by air showers during 690 days of operation and selected 820 proton-induced events with its primary energy above 200 TeV using a neural network method. Using this data set, we obtained the energy spectrum of primary protons in the energy range from 200 to 1000 TeV. The differential energy spectrum obtained in this energy region can be fitted by a power law with the index of -2.97 $\pm$ 0.06, which is steeper than that obtained by direct measurements at lower energies. We also obtained the energy spectrum of helium nuclei at particle energies around 1000 TeV.Comment: 25 pages, 22 figures, Accepted for publication in Phys. Rev.

Observation by an Air-Shower Array in Tibet of the Multi-TeV Cosmic-Ray Anisotropy due to Terrestrial Orbital Motion Around the Sun

We report on the solar diurnal variation of the galactic cosmic-ray intensity observed by the Tibet III air shower array during the period from 1999 to 2003. In the higher-energy event samples (12 TeV and 6.2 TeV), the variations are fairly consistent with the Compton-Getting anisotropy due to the terrestrial orbital motion around the sun, while the variation in the lower-energy event sample (4.0 TeV) is inconsistent with this anisotropy. This suggests an additional anisotropy superposed at the multi-TeV energies, e.g. the solar modulation effect. This is the highest-precision measurement of the Compton-Getting anisotropy ever made.Comment: 4 pages, 2 figures, includes .bbl fil

Observation of Multi-Tev Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array

Data from the Tibet-III air shower array (with energies around 3 TeV) and from the Tibet-II array (with energies around 10 TeV) have been searched for diffuse gamma rays from the Galactic plane. These arrays have an angular resolution of about 0.9 degrees. The sky regions searched are the inner Galaxy, 20 degrees <= l <= 55 degrees, and outer Galaxy, 140 degrees <= l <= 225 degrees, and |b| <= 2 degrees or <= 5 degrees. No significant Galactic plane gamma-ray excess was observed. The 99% confidence level upper limits for gamma-ray intensity obtained are (for |b| <= 2 degrees) 1.1 times 10^{-15} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 4.1 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the inner Galaxy, and 3.6 times 10^{-16} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 1.3 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the outer Galaxy, assuming a differential spectral index of 2.4. The upper limits are significant in the multi-TeV region when compared to those from Cherenkov telescopes in the lower energy region and other air shower arrays in the higher energy region; however, the results are not sufficient to rule out the inverse Compton model with a source electron spectral index of 2.0.Comment: 22 pages, 8 figures, Accepted for publication in Ap