Abstract:
This paper discusses the use of fat-tailed distributions in catastrophe prediction as opposed to the more common use of the Normal Distribution.

Abstract:
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to accurately calculate them by solving a functional equation concerning auxiliary fields which come out in an analysis based on replica/cavity methods. However, the difficulty in analytically solving this equation makes an accurate calculation infeasible in practice. To overcome this problem, we develop approximation schemes on the basis of two exceptionally solvable examples. The schemes are reasonably consistent with numerical experiments when the statistical bias of positive matrix entries is sufficiently large, and they qualitatively explain why considerably large finite size effects of the first eigenvalue can be observed when the bias is relatively small.

Abstract:
We review recent developments in non-perturbative field theory using modal field methods. We discuss Monte Carlo results as well as a new diagonalization technique known as the quasi-sparse eigenvector method.

Abstract:
We briefly review the diagonalization of quantum Hamiltonians using the quasi-sparse eigenvector (QSE) method. We also introduce the technique of stochastic error correction, which systematically removes the truncation error of the QSE result by stochastically sampling the contribution of the remaining basis states.

Abstract:
A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $\tau.$ We find that destroying all correlations without changing the $\tau = 1$ d distribution, by shuffling the order of the daily returns, causes the fat tails almost to vanish for $\tau>1$ d. We argue that the fat tails are caused by known long-range volatility correlations. Indeed, destroying only sign correlations, by shuffling the order of only the signs (but not the absolute values) of the daily returns, allows the fat tails to persist for $\tau >1$ d.

Abstract:
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second eigenvector of a matrix defined solely in terms of the incidence matrix, called the graph Laplacian. For sparse graphs, the eigenvector can be efficiently computed using the Lanczos algorithm. This graph partitioning algorithm is extended to provide a complete hierarchical subdivision of the graph. The method has been implemented and numerical results obtained both for simple test problems and for several grid graphs.

Abstract:
The aim of this article focuses on analyzing the implications of fat-tailed distributions in emerging capital markets. An essential aspect that was highlighted by most empirical research, especially in terms of emerging capital markets, emphasizes the fact that extreme financial events can not be accurately predicted by the normal distribution. Fat-tailed distributions establish a very effective econometric tool in the analysis of rare events which are characterized by extreme values that occur with a relatively high frequency .The importance of exploring this particular issue derives from the fact that it is fundamental for optimal portfolio selection, derivatives valuation, financial hedging and risk management strategies. The implications of fat-tailed distributions for investment process are significant especially in the turbulent context of the global financial crisis.

Abstract:
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regime of typical fluctuations by a phase transition where the symmetry between the points in the sample is spontaneously broken. For stochastic processes with a fat tailed microscopic noise, this implies that while typical realizations are well described by a diffusion process with continuous sample paths, large deviation paths are typically discontinuous. For eigenvalues of random matrices with fat tailed distributed elements, a large deviation where the trace of the matrix is anomalously large concentrates on just a single eigenvalue, whereas in the thin tailed world the large deviation affects the whole distribution. These results find a natural application to finance. Since the price dynamics of financial stocks is characterized by fat tailed increments, large fluctuations of stock prices are expected to be realized by discrete jumps. Interestingly, we find that large excursions of prices are more likely realized by continuous drifts rather than by discontinuous jumps. Indeed, auto-correlations suppress the concentration of large deviations. Financial covariance matrices also exhibit an anomalously large eigenvalue, the market mode, as compared to the prediction of random matrix theory. We show that this is explained by a large deviation with excess covariance rather than by one with excess volatility.

Abstract:
The performance of two fat-tailed sheep breeds, Chaal and Zandi, and their F1 and R1 crossbred lambs from a lean-tailed breed, Zel, was compared. The weaned lambs from the Chaal and Zandi groups were finished over periods of 105 and 90 days, respectively, and body weight gain and feed consumption were recorded. Forty six male and female lambs from the six finishing groups were slaughtered. The weights of blood, internal organs, intestines before and after removal of digesta, head, feet, pelt and carcasses were recorded. The left sides of the carcasses were cut into six pieces. Individual joints were dissected into lean meat, bone, subcutaneous fat (SCF), intramuscular fat (IMF) and trimmings, and weighed separately. The fat surrounding the intestine and kidney was weighed and considered as internal fat. All the soft tissue (lean meat and fat) of the left sides of the carcasses was ground and representative samples were taken for chemical analyses. The differences of eye muscle ( Longissimis dorsi ) area (cm2), and protein and bone percentages were not significant between both breeds and their crosses. In the R1 the fat-tail percentage was less than in the F1 and pure lambs of both breeds. In contrast, the SCF and IMF percentages were higher in all crossbred combinations. The internal fat percentages in crossbreds were higher, and in the Chaal group differed significantly from that of the pure lambs. The SCF/IMF ratio in the R1 lambs was lower than in the pure breds. This difference for Chaal crossbreds was significant. The lower ratio of SCF/IMF and the higher internal fat of crossbred lambs compared to pure breds showed that carcass quality of the crossbred was inferior compared to the pure bred lambs in terms of fat distribution in the body.