Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio

Activity autocorrelation in financial markets. A comparative study between several models

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Comment: 15 pages, 4 figure

Monitoring of the pre-equilibrium step in the alkyne hydration reaction catalyzed by au(Iii) complexes: A computational study based on experimental evidences

The coordination ability of the [(ppy)Au(IPr)]2+ fragment [ppy = 2-phenylpyridine, IPr = 1,3-bis(2,6-di-isopropylphenyl)-imidazol-2-ylidene] towards different anionic and neutral X ligands (X = Cl 12, BF4 12, OTf 12, H2 O, 2-butyne, 3-hexyne) commonly involved in the crucial pre-equilibrium step of the alkyne hydration reaction is computationally investigated to shed light on unexpected experimental observations on its catalytic activity. Experiment reveals that BF4 12 and OTf 12 have very similar coordination ability towards [(ppy)Au(IPr)]2+ and slightly less than water, whereas the alkyne complex could not be observed in solution at least at the NMR sensitivity. Due to the steric hindrance/dispersion interaction balance between X and IPr, the [(ppy)Au(IPr)]2+ fragment is computationally found to be much less selective than a model [(ppy)Au(NHC)]2+ (NHC = 1,3-dimethylimidazol-2-ylidene) fragment towards the different ligands, in particular OTf 12 and BF4 12, in agreement with experiment. Effect of the ancillary ligand substitution demonstrates that the coordination ability of Au(III) is quantitatively strongly affected by the nature of the ligands (even more than the net charge of the complex) and that all the investigated gold fragments coordinate to alkynes more strongly than H2 O. Remarkably, a stabilization of the water-coordinating species with respect to the alkyne-coordinating one can only be achieved within a microsolvation model, which reconciles theory with experiment. All the results reported here suggest that both the Au(III) fragment coordination ability and its proper computational modelling in the experimental conditions are fundamental issues for the design of efficient catalysts

An Iterative Method Based on Fractional Derivatives for Solving Nonlinear Equations

The theory of fractional order derivatives are almost as old as the integer-order [5]. There are many applications, for example in physics [1], [2], [6], finance [8], [9] or biology [3]. Our aim is not to use fractional order operators to modeling such things, we only will use them as a device to prove a theoretical mathematical statement. In this work our goal is to find a solution numerically for the equation A(u) = f . If we assume that u is time-dependent, then one can do this by finding a stationary solution of the equation ¶tu(t)

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulation

Common Scaling Patterns in Intertrade Times of U. S. Stocks

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution; (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form; (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anti-correlated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.Comment: 8 pages, 5 figures. Presented at The Second Nikkei Econophysics Workshop, Tokyo, 11-14 Nov. 2002. A subset appears in "The Application of Econophysics: Proceedings of the Second Nikkei Econophysics Symposium", editor H. Takayasu (Springer-Verlag, Tokyo, 2003) pp.51-57. Submitted to Phys. Rev. E on 25 June 200

A two-stage genome-wide association study of sporadic amyotrophic lateral sclerosis

The cause of sporadic amyotrophic lateral sclerosis (ALS) is largely unknown, but genetic factors are thought to play a significant role in determining susceptibility to motor neuron degeneration. To identify genetic variants altering risk of ALS, we undertook a two-stage genome-wide association study (GWAS): we followed our initial GWAS of 545 066 SNPs in 553 individuals with ALS and 2338 controls by testing the 7600 most associated SNPs from the first stage in three independent cohorts consisting of 2160 cases and 3008 controls. None of the SNPs selected for replication exceeded the Bonferroni threshold for significance. The two most significantly associated SNPs, rs2708909 and rs2708851 [odds ratio (OR) = 1.17 and 1.18, and P-values = 6.98 x 10–7 and 1.16 x 10–6], were located on chromosome 7p13.3 within a 175 kb linkage disequilibrium block containing the SUNC1, HUS1 and C7orf57 genes. These associations did not achieve genome-wide significance in the original cohort and failed to replicate in an additional independent cohort of 989 US cases and 327 controls (OR = 1.18 and 1.19, P-values = 0.08 and 0.06, respectively). Thus, we chose to cautiously interpret our data as hypothesis-generating requiring additional confirmation, especially as all previously reported loci for ALS have failed to replicate successfully. Indeed, the three loci (FGGY, ITPR2 and DPP6) identified in previous GWAS of sporadic ALS were not significantly associated with disease in our study. Our findings suggest that ALS is more genetically and clinically heterogeneous than previously recognized. Genotype data from our study have been made available online to facilitate such future endeavors

POMT2 mutations cause alpha-dystroglycan hypoglycosylation and Walker-Warburg syndrome

Background: Walker-Warburg syndrome (WWS) is an autosomal recessive condition characterised by congenital muscular dystrophy, structural brain defects, and eye malformations. Typical brain abnormalities are hydrocephalus, lissencephaly, agenesis of the corpus callosum, fusion of the hemispheres, cerebellar hypoplasia, and neuronal overmigration, which causes a cobblestone cortex. Ocular abnormalities include cataract, microphthalmia, buphthalmos, and Peters anomaly. WWS patients show defective O-glycosylation of α-dystroglycan (α-DG), which plays a key role in bridging the cytoskeleton of muscle and CNS cells with extracellular matrix proteins, important for muscle integrity and neuronal migration. In 20% of the WWS patients, hypoglycosylation results from mutations in either the protein O-mannosyltransferase 1 (POMT1), fukutin, or fukutin related protein (FKRP) genes. The other genes for this highly heterogeneous disorder remain to be identified. Objective: To look for mutations in POMT2 as a cause of WWS, as both POMT1 and POMT2 are required to achieve protein O-mannosyltransferase activity. Methods: A candidate gene approach combined with homozygosity mapping. Results: Homozygosity was found for the POMT2 locus at 14q24.3 in four of 11 consanguineous WWS families. Homozygous POMT2 mutations were present in two of these families as well as in one patient from another cohort of six WWS families. Immunohistochemistry in muscle showed severely reduced levels of glycosylated α-DG, which is consistent with the postulated role for POMT2 in the O-mannosylation pathway. Conclusions: A fourth causative gene for WWS was uncovered. These genes account for approximately one third of the WWS cases. Several more genes are anticipated, which are likely to play a role in glycosylation of α-DG

Identification of a deep intronic mutation in the COL6A2 gene by a novel custom oligonucleotide CGH array designed to explore allelic and genetic heterogeneity in collagen VI-related myopathies

BACKGROUND: Molecular characterization of collagen-VI related myopathies currently relies on standard sequencing, which yields a detection rate approximating 75-79% in Ullrich congenital muscular dystrophy (UCMD) and 60-65% in Bethlem myopathy (BM) patients as PCR-based techniques tend to miss gross genomic rearrangements as well as copy number variations (CNVs) in both the coding sequence and intronic regions. METHODS: We have designed a custom oligonucleotide CGH array in order to investigate the presence of CNVs in the coding and non-coding regions of COL6A1, A2, A3, A5 and A6 genes and a group of genes functionally related to collagen VI. A cohort of 12 patients with UCMD/BM negative at sequencing analysis and 2 subjects carrying a single COL6 mutation whose clinical phenotype was not explicable by inheritance were selected and the occurrence of allelic and genetic heterogeneity explored. RESULTS: A deletion within intron 1A of the COL6A2 gene, occurring in compound heterozygosity with a small deletion in exon 28, previously detected by routine sequencing, was identified in a BM patient. RNA studies showed monoallelic transcription of the COL6A2 gene, thus elucidating the functional effect of the intronic deletion. No pathogenic mutations were identified in the remaining analyzed patients, either within COL6A genes, or in genes functionally related to collagen VI. CONCLUSIONS: Our custom CGH array may represent a useful complementary diagnostic tool, especially in recessive forms of the disease, when only one mutant allele is detected by standard sequencing. The intronic deletion we identified represents the first example of a pure intronic mutation in COL6A genes