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Inference on the basis of high-dimensional and functional data are two topics which are discussed frequently in the current statistical literature. A possibility to include both topics in a single approach is working on a very general space for the underlying observations, such as a separable Hilbert space. We propose a general method for consistently hypothesis testing on the basis of random variables with values in separable Hilbert spaces. We avoid concerns with the curse of dimensionality due to a projection idea. We apply well-known test statistics from nonparametric inference to the projected data and integrate over all projections from a specific set and with respect to suitable probability measures. In contrast to classical methods, which are applicable for real-valued random variables or random vectors of dimensions lower than the sample size, the tests can be applied to random vectors of dimensions larger than the sample size or even to functional and high-dimensional data. In general, resampling procedures such as bootstrap or permutation are suitable to determine critical values. The idea can be extended to the case of incomplete observations. Moreover, we develop an efficient algorithm for implementing the method. Examples are given for testing goodness-of-fit in a one-sample situation in [1] or for testing marginal homogeneity on the basis of a paired sample in [2]. Here, the test statistics in use can be seen as generalizations of the well-known Cramérvon-Mises test statistics in the one-sample and two-samples case. The treatment of other testing problems is possible as well. By using the theory of U-statistics, for instance, asymptotic null distributions of the test statistics are obtained as the sample size tends to infinity. Standard continuity assumptions ensure the asymptotic exactness of the tests under the null hypothesis and that the tests detect any alternative in the limit. Simulation studies demonstrate size and power of the tests in the finite sample case, confirm the theoretical findings, and are used for the comparison with concurring procedures. A possible application of the general approach is inference for stock market returns, also in high data frequencies. In the field of empirical finance, statistical inference of stock market prices usually takes place on the basis of related log-returns as data. In the classical models for stock prices, i.e., the exponential Lévy model, Black-Scholes model, and Merton model, properties such as independence and stationarity of the increments ensure an independent and identically structure of the data. Specific trends during certain periods of the stock price processes can cause complications in this regard. In fact, our approach can compensate those effects by the treatment of the log-returns as random vectors or even as functional data.
Objective
Hemodialysis patients show an approximately threefold higher prevalence of cognitive impairment compared to the age-matched general population. Impaired microcirculatory function is one of the assumed causes. Dynamic retinal vessel analysis is a quantitative method for measuring neurovascular coupling and microvascular endothelial function. We hypothesize that cognitive impairment is associated with altered microcirculation of retinal vessels.
Methods
152 chronic hemodialysis patients underwent cognitive testing using the Montreal Cognitive Assessment. Retinal microcirculation was assessed by Dynamic Retinal Vessel Analysis, which carries out an examination recording retinal vessels' reaction to a flicker light stimulus under standardized conditions.
Results
In unadjusted as well as in adjusted linear regression analyses a significant association between the visuospatial executive function domain score of the Montreal Cognitive Assessment and the maximum arteriolar dilation as response of retinal arterioles to the flicker light stimulation was obtained.
Conclusion
This is the first study determining retinal microvascular function as surrogate for cerebral microvascular function and cognition in hemodialysis patients. The relationship between impairment in executive function and reduced arteriolar reaction to flicker light stimulation supports the involvement of cerebral small vessel disease as contributing factor for the development of cognitive impairment in this patient population and might be a target for noninvasive disease monitoring and therapeutic intervention.
It was generally believed that coal sources are not favorable as live-in habitats for microorganisms due to their recalcitrant chemical nature and negligible decomposition. However, accumulating evidence has revealed the presence of diverse microbial groups in coal environments and their significant metabolic role in coal biogeochemical dynamics and ecosystem functioning. The high oxygen content, organic fractions, and lignin-like structures of lower-rank coals may provide effective means for microbial attack, still representing a greatly unexplored frontier in microbiology. Coal degradation/conversion technology by native bacterial and fungal species has great potential in agricultural development, chemical industry production, and environmental rehabilitation. Furthermore, native microalgal species can offer a sustainable energy source and an excellent bioremediation strategy applicable to coal spill/seam waters. Additionally, the measures of the fate of the microbial community would serve as an indicator of restoration progress on post-coal-mining sites. This review puts forward a comprehensive vision of coal biodegradation and bioprocessing by microorganisms native to coal environments for determining their biotechnological potential and possible applications.
This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.
On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings.
Altered gastrocnemius contractile behavior in former achilles tendon rupture patients during walking
(2022)
Achilles tendon rupture (ATR) remains associated with functional limitations years after injury. Architectural remodeling of the gastrocnemius medialis (GM) muscle is typically observed in the affected leg and may compensate force deficits caused by a longer tendon. Yet patients seem to retain functional limitations during—low-force—walking gait. To explore the potential limits imposed by the remodeled GM muscle-tendon unit (MTU) on walking gait, we examined the contractile behavior of muscle fascicles during the stance phase. In a cross-sectional design, we studied nine former patients (males; age: 45 ± 9 years; height: 180 ± 7 cm; weight: 83 ± 6 kg) with a history of complete unilateral ATR, approximately 4 years post-surgery. Using ultrasonography, GM tendon morphology, muscle architecture at rest, and fascicular behavior were assessed during walking at 1.5 m⋅s–1 on a treadmill. Walking patterns were recorded with a motion capture system. The unaffected leg served as control. Lower limbs kinematics were largely similar between legs during walking. Typical features of ATR-related MTU remodeling were observed during the stance sub-phases corresponding to series elastic element (SEE) lengthening (energy storage) and SEE shortening (energy release), with shorter GM fascicles (36 and 36%, respectively) and greater pennation angles (8° and 12°, respectively). However, relative to the optimal fascicle length for force production, fascicles operated at comparable length in both legs. Similarly, when expressed relative to optimal fascicle length, fascicle contraction velocity was not different between sides, except at the time-point of peak series elastic element (SEE) length, where it was 39 ± 49% lower in the affected leg. Concomitantly, fascicles rotation during contraction was greater in the affected leg during the whole stance-phase, and architectural gear ratios (AGR) was larger during SEE lengthening. Under the present testing conditions, former ATR patients had recovered a relatively symmetrical walking gait pattern. Differences in seen AGR seem to accommodate the profound changes in MTU architecture, limiting the required fascicle shortening velocity. Overall, the contractile behavior of the GM fascicles does not restrict length- or velocity-dependent force potentials during this locomotor task.
This study aims to quantify the kinematics, kinetics and muscular activity of all-out handcycling exercise and examine their alterations during the course of a 15-s sprint test. Twelve able-bodied competitive triathletes performed a 15-s all-out sprint test in a recumbent racing handcycle that was attached to an ergometer. During the sprint test, tangential crank kinetics, 3D joint kinematics and muscular activity of 10 muscles of the upper extremity and trunk were examined using a power metre, motion capturing and surface electromyography (sEMG), respectively. Parameters were compared between revolution one (R1), revolution two (R2), the average of revolution 3 to 13 (R3) and the average of the remaining revolutions (R4). Shoulder abduction and internal-rotation increased, whereas maximal shoulder retroversion decreased during the sprint. Except for the wrist angles, angular velocity increased for every joint of the upper extremity. Several muscles demonstrated an increase in muscular activation, an earlier onset of muscular activation in crank cycle and an increased range of activation. During the course of a 15-s all-out sprint test in handcycling, the shoulder muscles and the muscles associated to the push phase demonstrate indications for short-duration fatigue. These findings are helpful to prevent injuries and improve performance in all-out handcycling.
Useful market simulations are key to the evaluation of diferent market designs existing of multiple market mechanisms or rules. Yet a simulation framework which has a comparison of diferent market mechanisms in mind was not found. The need to create an objective view on different sets of market rules while investigating meaningful agent strategies concludes that such a simulation framework is needed to advance the research on this subject. An overview of diferent existing market simulation models is given which also shows the research gap and the missing capabilities of those systems. Finally, a methodology is outlined how a novel market simulation which can answer the research questions can be developed.
Advances in polymer science have significantly increased polymer applications in life sciences. We report the use of free-standing, ultra-thin polydimethylsiloxane (PDMS) membranes, called CellDrum, as cell culture substrates for an in vitro wound model. Dermal fibroblast monolayers from 28- and 88-year-old donors were cultured on CellDrums. By using stainless steel balls, circular cell-free areas were created in the cell layer (wounding). Sinusoidal strain of 1 Hz, 5% strain, was applied to membranes for 30 min in 4 sessions. The gap circumference and closure rate of un-stretched samples (controls) and stretched samples were monitored over 4 days to investigate the effects of donor age and mechanical strain on wound closure. A significant decrease in gap circumference and an increase in gap closure rate were observed in trained samples from younger donors and control samples from older donors. In contrast, a significant decrease in gap closure rate and an increase in wound circumference were observed in the trained samples from older donors. Through these results, we propose the model of a cell monolayer on stretchable CellDrums as a practical tool for wound healing research. The combination of biomechanical cell loading in conjunction with analyses such as gene/protein expression seems promising beyond the scope published here.
Cell spraying has become a feasible application method for cell therapy and tissue engineering approaches. Different devices have been used with varying success. Often, twin-fluid atomizers are used, which require a high gas velocity for optimal aerosolization characteristics. To decrease the amount and velocity of required air, a custom-made atomizer was designed based on the effervescent principle. Different designs were evaluated regarding spray characteristics and their influence on human adipose-derived mesenchymal stromal cells. The arithmetic mean diameters of the droplets were 15.4–33.5 µm with decreasing diameters for increasing gas-to-liquid ratios. The survival rate was >90% of the control for the lowest gas-to-liquid ratio. For higher ratios, cell survival decreased to approximately 50%. Further experiments were performed with the design, which had shown the highest survival rates. After seven days, no significant differences in metabolic activity were observed. The apoptosis rates were not influenced by aerosolization, while high gas-to-liquid ratios caused increased necrosis levels. Tri-lineage differentiation potential into adipocytes, chondrocytes, and osteoblasts was not negatively influenced by aerosolization. Thus, the effervescent aerosolization principle was proven suitable for cell applications requiring reduced amounts of supplied air. This is the first time an effervescent atomizer was used for cell processing.
Exposure to prolonged periods in microgravity is associated with deconditioning of the musculoskeletal system due to chronic changes in mechanical stimulation. Given astronauts will operate on the Lunar surface for extended periods of time, it is critical to quantify both external (e.g., ground reaction forces) and internal (e.g., joint reaction forces) loads of relevant movements performed during Lunar missions. Such knowledge is key to predict musculoskeletal deconditioning and determine appropriate exercise countermeasures associated with extended exposure to hypogravity.
Motile cilia are hair-like cell extensions that beat periodically to generate fluid flow along various epithelial tissues within the body. In dense multiciliated carpets, cilia were shown to exhibit a remarkable coordination of their beat in the form of traveling metachronal waves, a phenomenon which supposedly enhances fluid transport. Yet, how cilia coordinate their regular beat in multiciliated epithelia to move fluids remains insufficiently understood, particularly due to lack of rigorous quantification. We combine experiments, novel analysis tools, and theory to address this knowledge gap. To investigate collective dynamics of cilia, we studied zebrafish multiciliated epithelia in the nose and the brain. We focused mainly on the zebrafish nose, due to its conserved properties with other ciliated tissues and its superior accessibility for non-invasive imaging. We revealed that cilia are synchronized only locally and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Even though synchronization is local only, we observed global patterns of traveling metachronal waves across the zebrafish multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right noses, unveiling a chiral asymmetry of metachronal coordination. To understand the implications of synchronization for fluid pumping, we used a computational model of a regular array of cilia. We found that local metachronal synchronization prevents steric collisions, i.e., cilia colliding with each other, and improves fluid pumping in dense cilia carpets, but hardly affects the direction of fluid flow. In conclusion, we show that local synchronization together with tissue-scale cilia alignment coincide and generate metachronal wave patterns in multiciliated epithelia, which enhance their physiological function of fluid pumping.
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.
The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.
Based on the European Space Agency (ESA) Science in Space Environment (SciSpacE) community White Paper “Human Physiology – Musculoskeletal system”, this perspective highlights unmet needs and suggests new avenues for future studies in musculoskeletal research to enable crewed exploration missions. The musculoskeletal system is essential for sustaining physical function and energy metabolism, and the maintenance of health during exploration missions, and consequently mission success, will be tightly linked to musculoskeletal function. Data collection from current space missions from pre-, during-, and post-flight periods would provide important information to understand and ultimately offset musculoskeletal alterations during long-term spaceflight. In addition, understanding the kinetics of the different components of the musculoskeletal system in parallel with a detailed description of the molecular mechanisms driving these alterations appears to be the best approach to address potential musculoskeletal problems that future exploratory-mission crew will face. These research efforts should be accompanied by technical advances in molecular and phenotypic monitoring tools to provide in-flight real-time feedback.
We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio’s components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio’s components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.
On the applicability of several tests to models with not identically distributed random effects
(2023)
We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.
Ambitious climate targets affect the competitiveness of industries in the international market. To prevent such industries from moving to other countries in the wake of increased climate protection efforts, cost adjustments may become necessary. Their design requires knowledge of country-specific production costs. Here, we present country-specific cost figures for different production routes of steel, paying particular attention to transportation costs. The data can be used in floor price models aiming to assess the competitiveness of different steel production routes in different countries (Rübbelke, 2022).
Market abstraction of energy markets and policies - application in an agent-based modeling toolbox
(2023)
In light of emerging challenges in energy systems, markets are prone to changing dynamics and market design. Simulation models are commonly used to understand the changing dynamics of future electricity markets. However, existing market models were often created with specific use cases in mind, which limits their flexibility and usability. This can impose challenges for using a single model to compare different market designs. This paper introduces a new method of defining market designs for energy market simulations. The proposed concept makes it easy to incorporate different market designs into electricity market models by using relevant parameters derived from analyzing existing simulation tools, morphological categorization and ontologies. These parameters are then used to derive a market abstraction and integrate it into an agent-based simulation framework, allowing for a unified analysis of diverse market designs. Furthermore, we showcase the usability of integrating new types of long-term contracts and over-the-counter trading. To validate this approach, two case studies are demonstrated: a pay-as-clear market and a pay-as-bid long-term market. These examples demonstrate the capabilities of the proposed framework.