Critical Analysis of Hypothesis Tests in Federal Information Processing Standard (140-2)

This work presents an analysis of the existing dependencies between the tests of the FIPS 140-2 battery. Two main analytical approaches are utilized, the first being a study of correlations through the Pearson’s correlation coefficient that detects linear dependencies, and the second one being a novel application of the mutual information measure that allows detecting possible non-linear relationships. In order to carry out this study, the FIPS 140-2 battery is reimplemented to allow the user to obtain p-values and statistics that are essential for more rigorous end-user analysis of random number generators (RNG).     

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.     

Hybrid paramagnetic-ferromagnetic quantum computer design based on electron spin arrays and a ferromagnetic nanostripe

Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both types of analysis are concentrated mostly on Pearson’s correlation coefficient and consequently intraday lead-lag relationships (where one of the variables in a pair is time-lagged) are also associated with them. Under the Efficient-Market Hypothesis such relationships are not possible as all information is embedded in the prices, but in real markets we find such dependencies. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson’s correlation coefficient. Mutual information is not only a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using New York Stock Exchange 100 data not only on an intraday level, but also for daily stock returns, which have usually been ignored.     

Multifractal analysis of the software evolution in software networks

As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.     

Ecosystems with mutually exclusive interactions self-organize to a state of high diversity

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general unknown. Using lichen communities as an example, we propose a model for the evolution of mutually excluding organisms that compete for space. We suggest that chainlike or cyclic invasions open for creation of spatially separated subpopulations that subsequently can lead to increased diversity. In contrast to its nonspatial counterpart, our model predicts robust coexistence of a large number of species. It is demonstrated that large species diversity can be obtained on evolutionary time scales, provided that interactions between species have spatial constraints. In particular, a phase transition to a sustainable state of high diversity is identified.     

Quantifying the Predictability of Visual Scanpaths Using Active Information Storage

Entropy-based measures are an important tool for studying human gaze behavior under various conditions. In particular, gaze transition entropy (GTE) is a popular method to quantify the predictability of a visual scanpath as the entropy of transitions between fixations and has been shown to correlate with changes in task demand or changes in observer state. Measuring scanpath predictability is thus a promising approach to identifying viewers’ cognitive states in behavioral experiments or gaze-based applications. However, GTE does not account for temporal dependencies beyond two consecutive fixations and may thus underestimate the actual predictability of the current fixation given past gaze behavior. Instead, we propose to quantify scanpath predictability by estimating the active information storage (AIS), which can account for dependencies spanning multiple fixations. AIS is calculated as the mutual information between a processes’ multivariate past state and its next value. It is thus able to measure how much information a sequence of past fixations provides about the next fixation, hence covering a longer temporal horizon. Applying the proposed approach, we were able to distinguish between induced observer states based on estimated AIS, providing first evidence that AIS may be used in the inference of user states to improve human–machine interaction.     

Stress–Strain Dependence of Cross-Linked Single-Phase Polyether Urethane

Stress–strain dependencies of cross-linked elastomers under stretching are considered. The capabilities to describe stress–strain plots of different types for elastomers, including curves with an inflection, by high-elasticity theories are examined. Limitations in the use of common high-elasticity models in the theoretical calculations of stress–strain plots are revealed. The analysis shows that the stress–strain plots with an inflection can be obtained with appropriate adjustment of the concept of finite chain extensibility. We propose a combined two-parameter model based on this concept and on the theory of high elasticity, taking into account the spatial constraints at the initial stage of stretching of the polymer network. Abilities of the new approach to describe the stress–strain dependencies in an adequate manner are demonstrated for five samples of cross-linked polyurethane over the entire range of strain under stretching.     

Categorical Exploratory Data Analysis: From Multiclass Classification and Response Manifold Analytics Perspectives of Baseball Pitching Dynamics

All features of any data type are universally equipped with categorical nature revealed through histograms. A contingency table framed by two histograms affords directional and mutual associations based on rescaled conditional Shannon entropies for any feature-pair. The heatmap of the mutual association matrix of all features becomes a roadmap showing which features are highly associative with which features. We develop our data analysis paradigm called categorical exploratory data analysis (CEDA) with this heatmap as a foundation. CEDA is demonstrated to provide new resolutions for two topics: multiclass classification (MCC) with one single categorical response variable and response manifold analytics (RMA) with multiple response variables. We compute visible and explainable information contents with multiscale and heterogeneous deterministic and stochastic structures in both topics. MCC involves all feature-group specific mixing geometries of labeled high-dimensional point-clouds. Upon each identified feature-group, we devise an indirect distance measure, a robust label embedding tree (LET), and a series of tree-based binary competitions to discover and present asymmetric mixing geometries. Then, a chain of complementary feature-groups offers a collection of mixing geometric pattern-categories with multiple perspective views. RMA studies a system’s regulating principles via multiple dimensional manifolds jointly constituted by targeted multiple response features and selected major covariate features. This manifold is marked with categorical localities reflecting major effects. Diverse minor effects are checked and identified across all localities for heterogeneity. Both MCC and RMA information contents are computed for data’s information content with predictive inferences as by-products. We illustrate CEDA developments via Iris data and demonstrate its applications on data taken from the PITCHf/x database.     

Recurrence quantification analysis of global stock markets

This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures.     

Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets

Construction of graph-based approximations for multi-dimensional data point clouds is widely used in a variety of areas. Notable examples of applications of such approximators are cellular trajectory inference in single-cell data analysis, analysis of clinical trajectories from synchronic datasets, and skeletonization of images. Several methods have been proposed to construct such approximating graphs, with some based on computation of minimum spanning trees and some based on principal graphs generalizing principal curves. In this article we propose a methodology to compare and benchmark these two graph-based data approximation approaches, as well as to define their hyperparameters. The main idea is to avoid comparing graphs directly, but at first to induce clustering of the data point cloud from the graph approximation and, secondly, to use well-established methods to compare and score the data cloud partitioning induced by the graphs. In particular, mutual information-based approaches prove to be useful in this context. The induced clustering is based on decomposing a graph into non-branching segments, and then clustering the data point cloud by the nearest segment. Such a method allows efficient comparison of graph-based data approximations of arbitrary topology and complexity. The method is implemented in Python using the standard scikit-learn library which provides high speed and efficiency. As a demonstration of the methodology we analyse and compare graph-based data approximation methods using synthetic as well as real-life single cell datasets.     

A method on calculating high-dimensional mutual information and its application to registration of multiple ultrasound images

Using mutual information as a criterion for medical image registration, which requires no prior segmentation or preprocessing, has been both theoretically and practically proved to be an effective method in these years. However, this technique is confined in registering two images and hard to apply to multiple ones. The reason is that unlike mutual information between two variables, high-dimensional mutual information is ill defined. In textbooks and theoretical essays, three-dimensional mutual information is proposed based on Venn diagram. Unfortunately, mutual information defined in this way is not necessarily nonnegative. In order to overcome the problem, in this paper, we introduce the mutual information matrix. By calculating its eigenvalues, high-dimensional mutual information is defined. This definition is nonnegative, bounded, and could be extended to higher dimensions, thus enables us to register more than three images. In the end, this definition is tested and proved to be effective on registration of multiple US images through simulation.     

Features of X-ray diffraction on sapphire single crystals with a nanostructured surface

Single-crystal sapphire plates with stepped nanostructures on the surface produced by thermal treatment and with a stochastically distributed surface roughness were studied by X-ray diffraction. It was found that the angular dependencies of intensities and half-widths of the curves of diffraction reflection measured under the Bragg geometry conditions appreciably changed versus the mutual orientation of the direction of propagation of the X-ray beam and the position of the steps, forming nanostructures on the surfaces of sapphire plates.     

Stable all-fiber dual-wavelength thulium-doped fiber laser and its coherent beam combination

We demonstrate which we believe the first investigation on mutual injection-locking and coherent combining of two thulium-doped fiber lasers. Mutual coherence between the two fiber lasers is established by means of mutual coupling through two 3 dB couplers. High combining efficiency of 99% for two fiber laser has been obtained, and the fringe contrast of the intensity pattern at the receiving plane is as high as 93%. The solution to scale to high power coherent beam combining is briefly discussed.     

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.     

Mutual injection locking and coherent beam combining of two thulium doped fiber lasers

We demonstrate which we believe the first investigation on mutual injection-locking and coherent combining of two thulium-doped fiber lasers. Mutual coherence between the two fiber lasers is established by means of mutual coupling through two 3 dB couplers. High combining efficiency of 99% for two fiber laser has been obtained, and the fringe contrast of the intensity pattern at the receiving plane is as high as 93%. The solution to scale to high power coherent beam combining is briefly discussed.     

Noise abatement measures at airports: Contributing factors and mutual dependence

Airports are known to cause noise-related environmental concerns, mostly because significant environmental impact correlated with operation of airports arises from aircraft generated noise. In order to address this concern, many airports have applied a variety of actions that alleviate negative effects of noise i.e. noise abatement measures (NAMs). Although there are similarities between airports applying some of the NAMs, numbers and types of applied measures are quite different among them. This paper focuses on finding statistical evidence to support the hypothesis that there is a significant correlation between applied NAMs and specific characteristics related to airports. To determine the reasons why airports apply NAMs, a logistic regression method was used on the data set for 246 European airports. As predictor variables, five specific characteristics related to airports (number of runways, number of aircraft movements, distance from the city, population of the city it serves, per capita gross domestic product (GDP) of the country an airport is located in), and ten NAMs based on their mutual dependencies were used. The results demonstrate a significant correlation between the applied NAMs and particular airport-related characteristics, but also between NAMs themselves. These findings can be used to determine the likelihood of applying a particular NAM to any airport, based on the characteristics that show a significant correlation with the corresponding NAM.     

Reflection from 1D quasi-periodical structures

A theoretical investigation of 1D stationary and transient quasi-periodical dielectric structures is presented. A new approach for solving the problem of field interaction with such structures common for both stationary and transient cases, based on integral equations for the fields in transient media, is proposed. Some special cases of quasi-periodical structures with doubled quasi-periodicity are investigated numerically, showing that an additional complexity of the structure allows to obtain good filtering properties with a small number of quasi-periods. Transient structures with the same spatial dependencies, but with a time-dependent permittivity were also investigated.     

Adjoint-based sensitivity analysis of quantities of interest of complex combustion models

An adjoint-based approach for the sensitivity analysis of complex reaction mechanisms is presented. It builds purely on the evaluation of the governing equations. No adjoint equations have to be derived explicitly. Instead, the required adjoint operator is constructed numerically. The approach can be utilised for various kinetic models and in existing codes with minimal implementation effort. All dependencies on the state and on model parameters are fully evaluated without simplifications. Sensitivities are calculated more efficiently and more robustly compared with the often-used brute-force method. The approach is demonstrated for a homogeneous (zero-dimensional) reactor with different complex reaction mechanisms including several reaction types.     

A virtual intersubband spin–flip spin–orbit coupling induced spin relaxation in GaAs (110) quantum wells

A spin relaxation mechanism is proposed based on a second-order spin–flip intersubband spin–orbit coupling together with the spin-conserving scattering. The corresponding spin relaxation time is calculated via the Fermi golden rule. It is shown that this mechanism is important in symmetric GaAs (110) quantum wells with high impurity density. The dependencies of the spin relaxation time on electron density, temperature and well width are studied with the underlying physics analyzed.     

Statistical calculations of tracer and intrinsic diffusion coefficients in concentrated alloys and estimates of microscopic parameters of diffusion from experimental data

The earlier-developed statistical theory of diffusion in concentrated alloys based on the master equation approach is generalized to treat tracer diffusion in binary alloys. The theory developed is used to describe concentration dependencies of both tracer and intrinsic diffusion coefficients and to estimate microscopic parameters of diffusion in alloys CuNi, CuZn and AgCd for which necessary experimental data are available. We show that all main features of strong and peculiar concentration dependencies of diffusion coefficients observed in these alloys are naturally explained by the theory. Signs and scales of interatomic interactions important for diffusion in these alloys are found to strongly depend on the ratio of atomic sizes of alloy components, and types of these dependencies agree with simple physical considerations. We also discuss physical reasons for sharp concentration dependencies of diffusion coefficients characteristic of real alloys.