Пространства Марины Цветаевой

The hallmarks of space in Tsvetaeva’s poetic world are vertical orientation, two-worldness (many-worldness), measurability, and “immensity”, often expressed by asymmetry. Tsvetaeva’s model of the double world is presented both in its pure form and in a multilayer one (the model of “matryoshka” according to Lotman) with a hierarchical vertical correlation of spaces. The vertical sets the plots, stylistics, system of characters, system of time and expectations of the reader. Tsvetaeva is a bright representative of irrational tendencies in art, which manifest themselves against the background of rational ones, through their violation. Thus, The Attempt of a Room (1926) builds on an imaginary effort to present a hexagonal box of a rendezvous, but fails. The last poem I Keep Repeating the First Verse… (1940) is a poetic reaction to the “mistake in counting”: there should be not six but seven souls at the table. In one of her poems, Tsvetaeva calls herself “one who has edited the miracle with numbers”. This formula aphoristically expresses the nature of creativity asfirst intuitive search, and then rational design. The mathematical calculation of the composition of her books is an analogue of the metric-stanzaic “frame” of her lyrics. In the given proportions she often uses a deliberate failure by one unit (for example, in the collection From Two Books she adds one extra poem, which was originally missing in these two books).

Markov chain Monte Carlo for petrophysical inversion

Stochastic petrophysical inversion is a method to predict reservoir properties from seismic data. Recent advances in stochastic optimization allow generating multiple realizations of rock and fluid properties conditioned on seismic data. To match the measured data and represent the uncertainty of the model variables, a large number of realizations is generally required. Stochastic sampling and optimization of spatially correlated models are computationally demanding. Monte Carlo methods allow quantifying the uncertainty of the model variables but are impractical for high-dimensional models with spatially correlated variables. We propose a Bayesian approach based on an efficient implementation of the Markov chain Monte Carlo method for the inversion of seismic data for the prediction of reservoir properties. The proposed Bayesian approach includes an explicit vertical correlation model in the proposal distribution. It is applied trace by trace and the lateral continuity model is imposed by using the previously simulated values at the adjacent traces as conditioning data for simulating the initial model at the current trace. The methodology is first presented for a one-dimensional problem to test the vertical correlation and it is extended to two-dimensional problems by including the lateral correlation and comparing two novel implementations based on sequential sampling. The proposed method is applied to synthetic data to estimate the posterior distribution of the petrophysical properties conditioned on the measured seismic data. The results are compared with a McMC implementation without lateral correlation and demonstrate the advantage of integrating a spatial correlation model.

Water modulates the lamellar structure and interlayer correlation of poly(perfluorooctyl acrylate) films: a specular and off-specular neutron scattering study

Comb-like polymers with pendant-like perfluorocarbon side chains self-assemble into smectic lamellae and have been extensively used as water-repellent, hydrophobic coating materials characterized by large water contact angles (θ > 120°). As poly(perfluorooctyl acrylate) films are “apparently hydrophobic” (θ > 120°), the interaction of such materials and water molecules has been largely overlooked. To unravel the molecular-level interactions between water and apparently hydrophobic polymers, specular and off-specular neutron scattering experiments were conducted at defined osmotic pressure ΠH2O. The poly{2-[(perfluorooctylethyl)carbamate]ethyl} acrylate (PFAUr-C8), which had a carbamate linker, transitioned to another lamellar phase at 89 °C. At T = 25 °C; the lamellar periodicity of PFAUr-C8 slightly increased with decreasing osmotic pressure, while the vertical correlation length increased. However, the poly[(perfluorooctyl)ethyl] acrylate (PFA-C8) that did not contain a carbamate linker directly transitioned to a disordered phase at 84 °C. The lamellar periodicity of PFA-C8 was largely independent of the osmotic pressure, suggesting that PFA-C8 was poorly hydrated. Remarkably, the vertical correlation length decreased with decreasing osmotic pressure. Because hydration facilitated by the linker modulated the smectic lamellae of the poly(perfluoroalkyl acrylate), water molecules could be used to optimize the self-assembly of apparently hydrophobic liquid crystalline polymers.

Using Dense Array Waveform Correlations to Build a Velocity Model with Stochastic Variability

ABSTRACT In an ongoing effort to improve 3D seismic-wave propagation modeling for frequencies up to 10 Hz, we used cross correlations between vertical-component waveforms from an underground chemical explosion to estimate the statistical properties of small-scale velocity heterogeneities. The waveforms were recorded by a dense 2D seismic array deployed during the Source Physics Experiments for event number 5 (SPE-5) in a series of six underground chemical explosions, conducted at the Nevada National Security Site. The array consisted of 996 geophones with a 50–100 m grid spacing, deployed at the SPE site at the north end of the Yucca Flat basin. The SPE were conducted to investigate the generation and propagation of seismic and acoustic waves from underground explosions. Comparisons of decay rates of waveform cross correlations as function of interstation distance, computed for observed and synthetic seismograms from the SPE-5 chemical explosion, were used to constrain statistical properties of correlated stochastic velocity perturbations representing small-scale heterogeneities added to a geology-based velocity model of the Yucca Flat basin. Using comparisons between recorded and simulated waveform cross correlations, we were able to recover sets of statistical properties of small-scale velocity perturbations in the velocity model that produce the best-fit between the recorded and simulated ground motion. The stochastic velocity fluctuations in the velocity model that produced the smallest misfits have a horizontal correlation distance of between 400 and 800 m, a vertical correlation distance between 100 and 200 m, and a standard deviation of 10% from the nominal model velocity in the alluvium basin layers. They also have a horizontal correlation distance of 1000 m, a vertical correlation distance of 250 m, and a standard deviation of 6% in the underlying and consolidated sedimentary layers, up to a depth of 4 km. Comparisons between observed and simulated wavefields were used to assess the proposed small-scale heterogeneity enhancements to the Yucca Flat basin model. We found that adding a depth-resolved stochastic variability to the geology-based velocity model improves the overall performance of ground-motion simulations of an SPE-5 explosion in the modeled frequency range up to 10 Hz. The results may be applicable to other similar basins.

The Poisson Link between Internal Wave and Dissipation Scales in the Thermocline. Part II: Internal Waves, Overturns, and the Energy Cascade

The irregular nature of vertical profiles of density in the thermocline appears well described by a Poisson process over vertical scales 2–200 m. To what extent does this view of the thermocline conflict with established models of the internal wavefield? Can a one-parameter Poisson subrange be inserted between the larger-scale wavefield and the microscale field of intermittent turbulent dissipation, both of which require many parameters for their specification? It is seen that a small modification to the Poisson vertical correlation function converts it to the corresponding correlation function of the Garrett–Munk (GM) internal wave spectral model. The linear scaling relations and vertical wavenumber dependencies of the GM model are maintained provided the Poisson constant κ0 is equated with the ratio of twice the displacement variance to the vertical correlation scale of the wavefield. Awareness of this Poisson wavefield relation enables higher-order strain statistics to be determined directly from the strain spectrum. Using observations from across the Pacific Ocean, the average Thorpe scale of individual overturning events is found to be nearly equal to the inverse of κ0, the metric of background thermocline distortion. If the fractional occurrence of overturning ϕ is introduced as an additional parameter, a Poisson version of the Gregg–Henyey relationship can be derived. The Poisson constant, buoyancy frequency, and ϕ combine to create a complete parameterization of energy transfer from internal wave scales through the Poisson subrange to dissipation. An awareness of the underlying Poisson structure of the thermocline will hopefully facilitate further improvement in both internal wave spectral models and ocean mixing parameterizations.

Statistical regularization for trend detection: an integrated approach for detecting long-term trends from sparse tropospheric ozone profiles

Detecting a tropospheric ozone trend from sparsely sampled ozonesonde profiles (typically once per week) is challenging due to the short-lived anomalies in the time series resulting from ozone's high temporal variability. To enhance trend detection, we have developed a sophisticated statistical approach that utilizes a geoadditive model to assess ozone variability across a time series of vertical profiles. Treating the profile time series as a set of individual time series on discrete pressure surfaces, a class of smoothing spline ANOVA (analysis of variance) models is used for the purpose of jointly modeling multiple correlated time series (on separate pressure surfaces) by their associated seasonal and interannual variabilities. This integrated fit method filters out the unstructured variation through a statistical regularization (i.e., a roughness penalty) by taking advantage of the additional correlated data points available on the pressure surfaces above and below the surface of interest. We have applied this technique to the trend analysis of the vertically correlated time series of tropospheric ozone observations from (1) IAGOS (In-service Aircraft for a Global Observing System) commercial aircraft profiles above Europe and China throughout 1994–2017 and (2) NOAA GML's (Global Monitoring Laboratory) ozonesonde records at Hilo, Hawaii, (1982–2018) and Trinidad Head, California (1998–2018). We illustrate the ability of this technique to detect a consistent trend estimate and its effectiveness in reducing the associated uncertainty in the profile data due to the low sampling frequency. We also conducted a sensitivity analysis of frequent IAGOS profiles above Europe (approximately 120 profiles per month) to determine how many profiles in a month are required for reliable long-term trend detection. When ignoring the vertical correlation, we found that a typical sampling strategy (i.e. four profiles per month) might result in 7 % of sampled trends falling outside the 2σ uncertainty interval derived from the full dataset with an associated 10 % of mean absolute percentage error. Based on a series of sensitivity studies, we determined optimal sampling frequencies for (1) basic trend detection and (2) accurate quantification of the trend. When applying the integrated fit method, we find that a typical sampling frequency of four profiles per month is adequate for basic trend detection; however, accurate quantification of the trend requires 14 profiles per month. Accurate trend quantification can be achieved with only 10 profiles per month if a regular sampling frequency is applied. In contrast, the standard separated fit method, which ignores the vertical correlation between pressure surfaces, requires 8 profiles per month for basic trend detection and 18 profiles per month for accurate trend quantification. While our method improves trend detection from sparse datasets, the key to substantially reducing the uncertainty is to increase the sampling frequency.

Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water

Array gain (AG) is significant in evaluating the detection performance of the vertical line array, which is directly determined by the correlation of signal and noise, respectively. In this paper, we analyze the vertical correlation for a 16-element vertical line array experimented in the deep ocean in 2016. The ray interference theory is utilized to interpret the mechanism of the vertical correlation of the sound field in different zones. In the direct-arrival zone, the direct rays and once-surface-reflected rays are two dominated components, whose arrival time difference for each element are nearly the same, and the vertical correlation is high. In the shadow zone, the sound field is mainly dominated by bottom-reflected rays and the vertical correlation decreases due to different grazing angles and arrival times of each ray. Different from the previous assumption of noise independence, the effect of noise correlation on the AG is analyzed through the measured marine environmental noise. Results indicate that the noise correlation coefficients in two zones are low but not 0. In the direct-arrival zone, AG is about 10 dB, very close to the ideal value of 10 log M . AG even exceeds it when NG is negative. Moreover, AG in the direct-arrival zone is higher than the one in the shadow zone.

Security Analysis of XOR Based Ciphered Image

In the present paper, we report security analysis of an effective method of scrambling i.e. XOR technique, which may be used as an important component in visual cryptography. Histogram of scrambled or encrypted images expressed that pixel values are distributed quite uniformly. This implies that nothing can be guessed about the original image using the encrypted image. For analyzing the complexity of encrypted images, information entropy, the correlation coefficient of adjacent pixels values were also calculated. Values of horizontal correlation, vertical correlation, and information entropy reflected that the complexity and randomness of pixel values are quite high for XOR cipher. Now a day’s differential attack has been very common. Keeping the same in the mind, we have calculated Unified Average Changing Intensity (UACI) and the Number of Pixels Change Rate (NPCR), to exhibit the ability of encrypted image using XOR cipher to resist the differential attack. So we can say that XOR cipher is useful for secure transmission of an image.