Assessing symmetry of financial returns series

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic T_n for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic T_n are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.     

Study of the K+π− total cross section for c.m. energy up to 3.4 GeV

The reaction K⁺p→Δ⁺⁺(1236) + anything is studied at a beam momentum of 16.0 GeV/c. The total and topological cross sections for K⁺π^? interactions are estimated by a Chew-Low extrapolation from threshold to the c.m. energy of 3.4 GeV by the maximum likelihood method.     

Cross sections for resonance production in the reaction πp → pπππ at 16 GeV/c, as obtained by a maximum likelihood fit: Aachen-Berlin-Bonn-CERN-Heidelberg Collaboration

Cross sections for resonance production in the reactions π^±p → pπ^±π⁺π⁻ at 16 GeV/c are determined by a maximum likelihood fit, making use of the measurements of all individual events. The reactions are described by a simple parametrization based on an incoherent superposition of amplitudes for quasi two-body and quasi three-body processes and a non-resonant backgroud. In this way the reflections are accounted for in a consistent way. Thus cross sections are obtained for Δ⁺⁺, Δ⁰, ρ⁰ and f⁰ production which do not suffer from the uncertainties of background subtraction typical of the usual technique of fitting individual mass distributions.     

The K+π- elastic scattering cross section as observed in K+p→K+π-Δ++ from 3 to 13 GeV/c

The four-body reaction K⁺p→K⁺π^-Δ⁺⁺ is analysed in a sample of 77 300 bubble chamber events of K⁺p→K⁺π^-π⁺p for beam momenta from 2.5 to 12.6 GeV/c to study the K⁺π^- elastic scattering cross section. The relative merits of several analytic continuations to the pion pole are discussed. Maximum likelihood method is used and, for each experiment fits are performed simultaneously over the whole range of the M(pπ⁺), m(K⁺π^-) and t variables. The K⁺π^- cross section is parametrized in terms of the down solution for the s-wave, a p-wave resonating at the K¹(890) and a d-wave resonating at the K¹(1420). Fitted values are obtained for the four-body cross section, the s-wave contribution to the K⁺π^- cross section, and the masses and widths of the K¹(890) and K¹(1420).     

Finite-N fluctuation formulas for random matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ _j ^N =1 (x _j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ _j ^N =1 (θ _j ?π) and ? Σ _j ^N =1 log 2 |sinθ _j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.     

Commutation superoperator of a state and its applications to the noncommutative statistics

For a normal state on a von Neumann algebra the space of square-integrable operators is introduced. As distinct from the L² space in the classical probability theory, it possesses an additional skew-symmetric form and the associated superoperator, which is a convenient tool to describe commutation properties in L². It is shown that a state on the algebra of canonical commutation relations is Gaussian (quasi-free) iff the space of canonical observables is an invariant subspace of the corresponding commutation superoperator. Basing on these ideas a new approach to some problems in the noncommutative statistic is developed.     

A test of the Lorentz structure of semi-hadronic τ decays

A method is proposed for the determination of the Lorentz structure of the electroweak interaction in semi-hadronic τ decays. Spin correlations in the process $$e^ + e^ - \to \tau ^ + \tau ^ - \to \bar v_\tau \pi ^ + \pi ^0 v_\tau \pi ^ - \pi ^0 $$ are exploited for a measurement of the normalized product, γ_AV = 2Re{g_Ag _V ^* }/(|g_V|² + |g_V|²), of the vector (g _V ) and axial vector (g _A ) coupling of the τ lepton. The contribution of scalar (g _S ) or pseudo-scalar (g _P ) couplings is also investigated. Since in the above process the direction of flight of the τ leptons can be reconstructed up to a twofold ambiguity a likelihood method using the whole kinematic information can be employed. The matrix element entering the likelihood function has been evaluated in terms of the momenta and angles of the observed pions. The sensitivity of the derived method in ane ⁺ e ^? energy region around 10 GeV has been investigated for the ARGUS experiment using Monte Carlo simulations.     

Transverse excitations in liquid Ga

The transverse acoustic excitation modes were detected by inelastic x-ray scattering in liquid Ga in the Q range above 9?nm^?1 although liquid Ga is mostly described by a hard-sphere liquid. An ab initio molecular dynamics simulation clearly supports this finding. From the detailed analysis for the S(Q,ω) spectra with a good statistic quality, the lifetime of 0.5 ps and the propagating length of 0.4–0.5?nm can be estimated for the transverse acoustic phonon modes, which may correspond the lifetime and size of cages formed instantaneously in liquid Ga. The microscopic Poisson’s ratio estimated from the dynamic velocities of sound is 0.42, indicating a rubber-like soft elastic property of the cages.     

City size distributions for India and China

This paper studies the size distributions of urban agglomerations for India and China. We have estimated the scaling exponent for Zipf’s law with the Indian census data for the years of 1981-2001 and the Chinese census data for 1990 and 2000. Along with the biased linear fit estimate, the maximum likelihood estimate for the Pareto and Tsallis q-exponential distribution has been computed. For India, the scaling exponent is in the range of [1.88, 2.06] and for China, it is in the interval [1.82, 2.29]. The goodness-of-fit tests of the estimated distributions are performed using the Kolmogorov-Smirnov statistic.     

A study of the Regge recurrence of the Δ(1236) produced in 10 GeV/c K+p interactions

Data are presented on a high mass $\text{I}\text{3}\text{2}\text{Δ}$ resonance produced in 10 GeV/c K⁺p interactions. The mass and width of the resonance, determined by a maximum likelihood fit to the pπ⁺ spectrum in the final state K⁺pπ⁺π^?, are 1895±15 MeV/c²230±50 MeV/c² respectively. The differential cross sections, dσ/dt, for the quasi two-body final states K¹(890)Δ(1236) and K¹(890)Δ(1900) are well described by the one pion exchange model. In addition the moments of the Gottfried-Jackson angular distribution of the pπ⁺ system agree with those computed from on-shell π⁺p elastic scattering data. We conclude that the two final states are produced mainly by π exchange and associate the structure observed in the moments up to NH(6,0) in the 1900 MeV region with the $\text{7}\text{2}{}^{\mathrm{+}}$ Regge recurrence of the Δ(1236). The dominant decay mode of the resonance is Δ⁺⁺(1900)→pπ⁺ but decays to pπ⁺π⁰ and nπ⁺π⁺ are also observed. Cross sections are determined for the production of the quasi two-body final states K¹(890)Δ(1236), K¹(890) Δ(1900), K¹(1420)Δ(1236) and K¹(1420)Δ(1900).     

A quantitative occam's razor

Interpreting entropy as a prior probability suggests a universal but “purely empirical” measure of “goodness of fit.” This allows statistical techniques to be used in situations where the correct theory- and not just its parameters-is still unknown. As developed illustratively for least-squares nonlinear regression, the measure proves to be a transformation of theR ² statistic. Unlike the latter, however, it diminishes rapidly as the number of fitting parameters increases.     

Field emission characteristics of thin-metal-coated nano-sheet carbon films

Nano-sheet carbon films (NSCFs) coated with very thin (≈5-nm-thick) metal layers were fabricated on Si wafer chips by means of quartz-tube-type microwave-plasma chemical-vapour-deposition method with hydrogen-methane gas mixture and an electron beam evaporation method. Field emission (FE) current densities obtained at a macroscopic average electric field, E, of ≈10 V/μm changed from 13 mA/cm² for NSCF with no coated metal to 1.7, 0.7 and 30 mA/cm² for Ti-, Al- and Au-coated NSCFs, respectively, while the threshold E varied from 4.4 V/μm for the former one to 5.3, 5.4 and 2.0 V/μm for the corresponding latter ones, respectively. As the FE currents of Au-coated NSCFs tended to be saturated in a higher E region, compared to those of NSCFs with no coated metal, no simple Fowler-Nordheim (F-N) model is applicable. A modified F-N model considering statistic effects of the FE tip structures and a space-charge-limited-current effect is successfully applied to an explanation for the FE data observed in the low and high E regions.     

Experimental test of the PCAC hypothesis in the reactionsv μ p→ μ− pπ+ and \bar v_\mu p \to \mu ^ + p\pi ^ - in theΔ(1232) region

Data on the reactionsv _μ p→ μ^? pπ⁺ and \( \bar v_\mu p \to \mu ^ + p\pi ^ - \) in the Δ(1232) region are presented and a test of the PCAC hypothesis, using a modified version of the Adler model, is performed. The analysis is based on 1081 events in the neutrino and on 180 events in the antineutrino reaction, obtained in a bubble chamber experiment with BEBC at CERN. The experimental cross-sections for an invariant hadronic massW<1.4 GeV and an (anti-)neutrino energyE _v ^L >10 GeV are determined to be (0.628±0.059)·10^?38 cm² for the neutrino and (0.168±0.023)·10^?38 cm² for the antineutrino reaction. TheQ ² andW distributions, the density matrix elements of the Δ resonance, and moments of the pion angular distribution are discussed. The data are found to be in good agreement with the Adler model in theQ ² region below 1 GeV². A maximum likelihood fit for the axial massm _A in the axial-vector form factor yields a value ofm _A =1.31±0.12 GeV. At lowQ ² the data confirm the PCAC hypothesis and the discrepancy, formerly observed between the experimental and theoretical cross-sections forv _μ p→ μ^? pπ⁺ at low momentum transfers (Q ²?0.2 GeV²), is understood as being due to inadequate pion ‘off-mass-shell’ corrections.     

A simple event weighting technique: optimizing the measurement of the forward-backward asymmetry of Drell-Yan dilepton and top-antitop pairs at hadron colliders

We describe a simple technique for optimizing the extraction of the forward-backward asymmetry (A _fb) of Drell-Yan lepton pairs (e ⁺ e ^?, μ ⁺ μ ^?) produced in $\bar{p}p$ and pp collisions at hadron colliders. The method employs simple event weights which are functions of the rapidity and |cos?θ| decay angle of the lepton pair. It yields the best estimate of the acceptance corrected parton level ( $\bar{q}q$ ) forward backward asymmetry as a function of final state dilepton mass (M _{? ?} ). Typically, when compared to the simple count method, the technique reduces the statistical errors by 20% for $\bar{p}p$ , and 40% for pp collisions, respectively. The method is equivalent to using the maximum likelihood method, but is much easier to implement. The technique can be used to search for new high mass and large width Z’ bosons which may be best detected through the observation of deviations from the Standard Model expectation for the forward-backward asymmetry. The technique can also be applied in the extraction of the foward-backward asymmetry in the production of top-antitop pairs.     

Using the modified sample entropy to detect determinism

A modified sample entropy (mSampEn), based on the nonlinear continuous and convex function, has been proposed and proven to be superior to the standard sample entropy (SampEn) in several aspects. In this Letter, we empirically investigate the ability of the mSampEn statistic combined with surrogate data method to detect determinism. The effects of the datasets length and noise on the proposed method to differentiate between deterministic and stochastic dynamics are tested on several benchmark time series. The noise performance of the mSampEn statistic is also compared with the singular value decomposition (SVD) and symplectic geometry spectrum (SGS) based methods. The results indicate that the mSampEn statistic is a robust index for detecting determinism in short and noisy time series.     

Five-pion final state in pp annihilations at 0.70 to 1.1 GeV/c

Results are reported on the reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ at six lab momenta spanning the region from 0.686 to 1.098 GeV/c. The cross section for this process drops from 20.3 ± 1.2 mb at 0.686 GeV/c to 13 1.0 mb at 1.098 GeV/c. Resonance production is determined by means of a model which includes Bose symmetrization, Breit-Wigner amplitudes and Bose-Einstein correlations for the like-charged pion pairs in the nonresonant part of the amplitude. The likelihood fit to the resonance channels yields about 0.8% ηππ, 12% ?^±πππ, 2% fπππ, 8% ωππ, 22% ?^±?⁰π, 13% ω?⁰ and 9% ωf with errors on the order of a few percent. Several percent A₁^±ππ and X(1440)π were also needed to obtain good fits. The ?⁰πππ and ?⁰?⁰π channels as well as A₂ππ and A₁⁰ππ are consistent with zero. Reasonable fits to the mass distributions are obtained. Production angular distributions are found to be essentially uniform. The angular correlations between pion pairs are approximately fit by the simple model of resonance production with Bose symmetrization.     

Study of the η'→Ve~+e~- decay with hidden local symmetry model

Within the hidden local symmetry framework, the Dalitz decay η→Ve+e-is studied with the vector meson dominance model. It is found that the partial width Γ(η→ωe+e-)≈40 e V and branching ratio B(η→ωe+e-)≈2×10-4, and Γ(η→ρe+e-)≈10Γ(η→ωe+e-) and B(η→ρe+e-)≈10B(η→ωe+e-). The maximum position of the dilepton distribution is m e+e-≈1.33 Me V. These decays are measurable with the advent of high statistic ηexperiments.     

Dissipative or conservative cosmology with dark energy?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property—acceleration—is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a one-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We characterize the class of dark energy models that admit late time de Sitter attractor solution in terms of the potential function of corresponding conservative system. We argue that inclusion of dissipation effects makes the model more realistic because of its structural stability. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the χ² function which is illustrated by residuals and χ² levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of χ² statistic are comparable for both the viscous model and ΛCDM model. The Bayesian information criteria are used to compare the models with different power-law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the ΛCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.     

基于TD-ERCS混沌系统的伪随机数发生器及其统计特性分析

为了进一步分析切延迟椭圆反射腔映射系统(TD-ERCS)混沌系统的密码学意义上的安全性， 采用TD-ERCS并行方式构造了一个结构简单的伪随机序列发生器.用户密码不再是固定不变的 ，可在［2⁶⁴，2⁶⁷²］区域内任意取值.对所产生的二值伪随机 序列（即TD-ERC S序列）进行了均衡性、游程特性、相关性等基本统计特性初步测试，并与m序列、logistic 序列、Chebyshev混沌序列、SCQC序列作了对比分析.实验表明，TD-ERCS序列有更好的统计 特性. 关键词： 混沌 TD-ERCS PRNG 统计特性     

Effect of electrostatic interaction on the methylene blue and methyl orange adsorption by the pristine and functionalized carbon nanotubes

Multi-walled carbon nanotubes (MWCNTs) were functionalized with cysteamine groups by several percentage of mass as adsorbents, then kinetics adsorption capacity was investigated for methylene blue (MB) and methyl orange (MO) as anionic and cationic dyes adsorbate molecules, respectively. The effect of temperature (from 283 to 303 K), contact time and initial concentration of the MB and MO dyes in a solution (10 to 40 ppm) was considered. The optimal contact time was found to be about 60 min. Some kinetics model such as pseudo-first-order, pseudo-second-order, intra-particle diffusion and the Elovich were tested. The adsorptions of MB dye on the pristine and functionalized MWCNT surfaces were found to be the intra-particle diffusion and the pseudo-second-order kinetic model, respectively and for adsorption of MO dye by the pristine and low functionalized MWCNTs and highly functionalized tubes, found to be the pseudo-second-order and intra-particle diffusion kinetic model, respectively, based on the chi-square statistic (X²) and also high correlation coefficient (R²) values.