Scaling Assumptions Research Articles

Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics

<i>Background</i>: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. <i>Objective</i>: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. <i>Method</i>: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. <i>Result</i>: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. <i>Conclusion</i>: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.

Reduced energies for thin ferromagnetic films with perpendicular anisotropy

We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction. Starting with a microscopic model that regularizes the stray field near the material’s lateral edges, we carry out an asymptotic analysis of the energy by means of [Formula: see text]-convergence. Depending on the scaling assumptions on the size of the material domain versus the strength of dipolar interaction, we obtain a hierarchy of the limit energies that exhibit progressively stronger stray field effects of the material edges. These limit energies feature, respectively, a renormalization of the out-of-plane anisotropy, an additional local boundary penalty term forcing out-of-plane alignment of the magnetization at the edge, a pinned magnetization at the edge, and, finally, a pinned magnetization and an additional field-like term that blows up at the edge, as the sample’s lateral size is increased. The pinning of the magnetization at the edge restores the topological protection and enables the existence of magnetic skyrmions in bounded samples.

How emotion is experienced and expressed in multiple cultures: a large-scale experiment across North America, Europe, and Japan.

Core to understanding emotion are subjective experiences and their expression in facial behavior. Past studies have largely focused on six emotions and prototypical facial poses, reflecting limitations in scale and narrow assumptions about the variety of emotions and their patterns of expression. We examine 45,231 facial reactions to 2,185 evocative videos, largely in North America, Europe, and Japan, collecting participants' self-reported experiences in English or Japanese and manual and automated annotations of facial movement. Guided by Semantic Space Theory, we uncover 21 dimensions of emotion in the self-reported experiences of participants in Japan, the United States, and Western Europe, and considerable cross-cultural similarities in experience. Facial expressions predict at least 12 dimensions of experience, despite massive individual differences in experience. We find considerable cross-cultural convergence in the facial actions involved in the expression of emotion, and culture-specific display tendencies-many facial movements differ in intensity in Japan compared to the U.S./Canada and Europe but represent similar experiences. These results quantitatively detail that people in dramatically different cultures experience and express emotion in a high-dimensional, categorical, and similar but complex fashion.

An improved equilibrium efficient frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

In recent years, significant development has been made in efficiency evaluation for Decision-Making Units (DMUs) with fixed-sum outputs. The Generalized Equilibrium Efficient Frontier Data Envelopment Analysis (GEEFDEA) approach introduced by Yang et al. (2015) is one of the most representative methods. In the GEEFDEA approach, all DMUs are adjusted to become efficient under the same set of weights, indicating that the Equilibrium Efficient Frontier (EEF) constructed consists of only one hyperplane. However, in practical scenarios under the Variable Return to Scale (VRS) assumption, the production frontier always consists of multiple hyperplanes, presenting a more complex shape. To fill this research gap, we propose an improved Equilibrium Efficient Frontier Data Envelopment Analysis approach. Our approach allows DMUs to have different weights for inputs, variable-sum outputs, and fixed-sum outputs, resulting in an EEF with multiple hyperplanes. It is noted that our new approach uses a non-linear model to obtain the EEF. We show that the model can be linearized in the case of a single fixed-sum output. In situations involving multiple fixed-sum outputs, we propose an algorithm based on the Expectation Maximization (EM) mechanism to solve the model to obtain an EEF. Finally, we illustrate the advantages of our new approach through a numerical example and a case study in the global motor vehicle industry.

The Nuances of Plant Disease Severity Estimation Using Quantitative Ordinal Scales-Lessons Learned over Four Decades.

We revisit the foundations of the Horsfall-Barratt (HB) scale, a widely cited and applied plant disease visual assessment tool introduced in 1945, a full 37 years prior to T. T. Hebert's 1982 critique that raised concerns regarding the scale's rationale, particularly its reliance on the Weber-Fechner law and visual perception assumptions. Although use of the HB scale and similar ordinal scales persists, comprehensive studies have revealed that direct visual estimation using percentage scales often proves more accurate and reliable. Challenges remain, such as biases due to estimator subjectivity and the potential for misclassification. The logarithmic assumptions of the HB scale have been debunked, and the importance of choosing appropriate interval sizes and numbers of classes in developing ordinal scales is emphasized. Analyzing ordinal scale data appropriately is crucial, and recent advances offer promising methods that reduce type II error rates. The closely related disease severity index is noted to have its shortcomings and potential for misuse. The letter underscores the need for continuous refinement and critical evaluation of disease assessment methodologies.

Toward mapping turbulence in the intra-cluster medium

Context. Future X-ray observatories with high spectral resolution and imaging capabilities will enable measurements and mappings of emission line shifts in the intracluster medium (ICM). Such direct measurements can serve as unique probes of turbulent motions in the ICM. Determining the level and scales of turbulence will improve our understanding of the galaxy cluster dynamical evolution and assembly, together with a more precise evaluation of the non thermal support pressure budget. This will allow for more accurate constraints to be placed on the masses of galaxy clusters, among other potential benefits. Aims. In this view, we implemented the methods presented in the previous instalments of our work to characterising the turbulence in the intra-cluster medium in a feasibility study with the X-ray Integral Field Unit (X-IFU) on board the future European X-ray observatory, Athena. Methods. From idealized mock observations of a toy model cluster, we reconstructed the second-order structure function built with the observed velocity field to constrain the turbulence. We carefully accounted for the various sources of errors to derive the most realistic and comprehensive error budget within the limits of our approach. With prior assumptions on the dissipation scale and power spectrum slope, we constrained the parameters of the turbulent power spectrum model through the use of Markov chain Monte Carlo (MCMC) sampling. Results. With a very long exposure time, a favourable configuration, and a prior assumption of the dissipation scale, we were able to retrieve the injection scale, velocity dispersion, and power spectrum slope, with 1σ uncertainties for better than ∼15% of the input values. We demonstrated the efficiency of our carefully set framework to constrain the turbulence in the ICM from high-resolution X-ray spectroscopic observations, paving the way for more in-depth investigation of the optimal required observing strategy within a more restrictive observational setup with the future Athena/X-IFU instrument.

A Variational Perspective on Auxetic Metamaterials of Checkerboard-Type

The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the obtained energy estimates are rather standard, determining the effective deformation behavior, or in other words, characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components, is the challenging part. To this end, we establish an asymptotic rigidity result, showing that, under suitable scaling assumptions, the attainable macroscopic deformations are affine conformal contractions. This identifies the composite as a mechanical metamaterial with a negative Poisson’s ratio. Our proof strategy is to tackle first an idealized model with full rigidity on the stiff tiles to acquire insight into the mechanics of the model and then transfer the findings and methodology to the model with diverging elastic constants. The latter requires, in particular, a new quantitative geometric rigidity estimate for non-connected squares touching each other at their vertices and a tailored Poincaré type inequality for checkerboard structures.

Input allocative efficiencies for operation and maintenance of rural piped water supply systems in highland areas of Vietnam

Strengthening the functioning of existing rural piped water supply systems is a critical strategy for ensuring household water security, particularly in water-scarce contexts. Improving operation and maintenance (O&M) of the systems is an important area of focus, commonly plagued by poor reliability and functionality over time. From an economic perspective, there is an opportunity to optimise O&M input efficiencies as a foundation for improved management. This paper presented challenges and opportunities to optimise O&M input efficiencies based on an analysis of water supply systems in Vietnam’s highland areas characterised by mountainous terrain and water scarcity. The analysis focused on state-based agencies for O&M given their mandate for restoring the inefficient systems and identified input norms for guidance on how to optimise O&M activities. We applied an input-oriented data envelopment analysis (DEA) model under constant returns to scale assumption to estimate technical, economic and allocative efficiencies. The results identified efficiency levels of 90%, 30% and 33% respectively. The study suggests a 10% reduction in general input amounts and identified efficient input target values reveal potential reduction rates for technical labour (12%), electricity (12%), as well as the technical and economic norms of technical labour (0.86 person- day∙(100 m3)–1 water sold) and electricity (0.53 kWh∙m–3 water sold). The policy implications for O&M state-based agencies include the adoption of input-based contracting mechanisms, while the government is encouraged to approve water tariffs and provide compensation based on input items to promote water service supply as a public good in water- scarce and challenging areas.

Level of technical efficiency and associated factors among health centers in East Gojjam Zone, Northwest Ethiopia: an application of the data envelopment analysis

BackgroundBesides the scarcity of resources, inefficient utilization of available health service resources has been the bottleneck to deliver quality health services in Ethiopia. However, Information regarding the efficiency of health service providers is limited in the country. Health service managers and policy makers must be well informed about the efficiency of health service providers and ways of using limited resources efficiently to make evidence-based decisions. This study aimed to assess the level of technical efficiency and associated factors among health centers in East Gojjam Zone, Northwest Ethiopia.MethodsA facility-based cross-sectional study was conducted among 27 randomly selected health centers in East Gojjam zone, Northwest Ethiopia, from October 30, 2022, to April 30, 2023. Using an interviewer-administered questionnaire and document review checklist, health centers’ data was collected and entered to Epi-Data version 4.6. The data was exported to Microsoft office excel and Stata version 14 for analysis. A two-stage output-oriented data envelopment analysis with a variable return to scale assumption was employed to determine the level of technical efficiencies. Finally, the tobit regression model was applied to identify the associated factors at 5% level of significance.ResultsIn this study, 59.3% of the health centers were technically efficient. The mean technical efficiency score of the health centers was 0.899 ± 0.156. Inefficient health centers could provide more 22, 433 outpatient visits, 1,351 family planning visits, 155 referral services, 206 skilled deliveries and 385 fully vaccinations of children if they were technically efficient as their peer health centers for the same year. From the tobit regression, the catchment population and number of administrative staffs were statistically significant determinants of the technical efficiency of health centers.ConclusionsThe mean technical efficiency of the health centers in East Gojjam zone, Northwest Ethiopia was high. However, nearly half of the health centers were technically inefficient, which indicates the exitance of a space for further improvements in the productivity of these health centers. Employing excess number administrative staffs (above the optimal level) should be discouraged and selecting appropriate sites where the health centers to be constructed (to have large catchment population coverage) could improve the productivity of health centers.

Optimization of business strategy in improving the efficiency of business capital use

Indonesia is the fourth largest coffee-producing country in the world after Brazil, Vietnam, and Colombia (Richardson et al., 2023). Seeing this opportunity is widely used by business people in making coffee shops (Fahmi & Savira, 2023). This study aims to see the level of efficiency produced by coffee shops with data envelopment analysis (DEA) techniques. This analysis uses input variables, namely labor costs, raw material costs, overall capital, and the amount of labor, and output variables, namely gross profit, and net profit. In DEA using variable return scale (VRS) assumptions where the addition of inputs is not necessarily offset by the output. The sample used was 67 coffee shops in Soloraya. The results of the analysis show that 22 coffee shops have experienced a 100 percent efficiency level while 45 coffee shops have not experienced a 100 percent efficiency level, meaning that those that have not reached 100 percent need improvement in the use of inputs and improved output targets and also benchmarking to make adjustments to their business activities. Managers find it easier to make decisions about whether the business will be saved or increased targets so DEA techniques are more suitable for business people to use in making a decision.

Efficiency of Mutual Funds and Portfolio Performance Measurement: A Case of Selected Mutual Funds in Tanzania

This study examines the current efficiency trends in the Tanzanian mutual fund industry over a five-year span (2018-2022), focusing on six specific funds: Umoja Fund, WekezaMaisha, Watoto Fund, Jikimu Fund, Liquid Fund, and Bond Fund. Employing a non-parametric approach, specifically Data Envelopment Analysis (DEA), the research collects secondary data from diverse sources, including newspapers, journals, books, periodicals, and the websites of UTT and the Bank of Tanzania (BOT). Monthly Net Asset Values (NAVs) of the selected mutual funds are scrutinized from each scheme's inception. Motivated by the limited understanding of mutual fund efficiency in Tanzania despite reported successes in increased asset values, profitability, and investor numbers, the study reveals distinctive performances under Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) assumptions. Under VRS, all mutual funds consistently achieve nearly 100% efficiency, signifying optimal operational scales. However, under CRS, efficiency scores fluctuate over time, underscoring the importance of mutual funds' adaptability for enhanced efficiency. Furthermore, the research suggests that mutual fund size significantly influences efficiency and potential scale economies. Smaller mutual funds demonstrate superior resource utilization efficiency, attributed to their focused investment approach. The analysis of inputs and output slacks provides insights into efficiency and resource utilization, identifying areas of optimal resource management and highlighting opportunities for improvement. The findings offer valuable insights into mutual fund efficiency under different scale assumptions, emphasizing the importance of scale flexibility and efficient resource management for superior performance. Implications suggest avenues for further research to explore external factors, efficiency fluctuations, portfolio management practices, and longitudinal trends within the mutual fund industry.

No evidence for fractal scaling in canopy surfaces across a diverse range of forest types

Abstract Canopy structural complexity is a key emergent property of forest ecosystems that directly relates to their ability to store carbon, cycle water and nutrients, and provide habitat for biodiversity. However, we lack a general framework for quantifying the structural complexity of forest canopies, and it remains to be seen if there are simple rules that explain the huge variation in canopy structure that we observe across the world's forests. A leading candidate for characterizing differences in structural complexity among forest ecosystems are fractal scaling laws, or measures of statistical self‐similarity. If forest canopies were fractal in nature, their structural attributes could be distilled into a single coefficient—their fractal dimension—which could then be used to directly compare structural differences within and across biomes. To test this idea, we used airborne laser scanning (ALS) data acquired across nine landscapes in Australia that span a huge environmental gradient and include everything from dry shrublands, tropical savannas, dense rainforests, to 90 m tall Mountain Ash forests. Using the ALS data, we built high‐resolution 3D canopy height models of each landscape so that we could quantify how closely they followed fractal scaling laws, based on a comprehensive set of fractal dimension estimators. Across all ecosystem types, fractal scaling assumptions were consistently violated, with clear and systematic differences between real‐world forest canopies and simulated fractal surfaces. However, deviations from fractality did vary predictably among sites, with forests in less arid environments, dominated by tall trees with large crowns, exhibiting a higher degree of self‐similarity across scales. Synthesis: Our study conclusively shows that canopy surfaces are not fractal beyond the scale of individual tree crowns. Nevertheless, we still observed ecologically meaningful and generalisable patterns in forest structure across scales, which closely reflect biophysical and physiological constraints on tree size and architecture. These patterns point the way towards a more general framework for characterizing ecological complexity.

Generation of Artificial ULF/ELF Electromagnetic Emission in the Ionosphere by Horizontal Ground‐Based Current System

AbstractThe feasibility of the detection of electromagnetic response in the upper ionosphere to ground large‐scale ultra‐low‐frequency (ULF) and extremely‐low‐frequency (ELF) transmitters by low‐Earth‐orbit (LEO) satellites is considered. As an example of such transmitters, we consider the ZEVS 82 Hz transmitter, FENICS installation driven by 0.5–150 Hz generator, and industrial 50 Hz unbalanced power transmission lines. We numerically model the ULF/ELF wave energy leakage into the upper ionosphere from an oscillating grounded linear power line of a finite length suspended above a ground with a finite resistivity. The numerical scheme is based on the theoretical formalism developed to describe the excitation of an electromagnetic field by a horizontal grounded dipole. A realistic altitudinal profile of the plasma parameters has been reconstructed with the use of the IRI ionospheric model. For the ZEVS transmitter powered by 200 A current the modeled amplitudes of electromagnetic response can reach in the upper nightside ionosphere up to 60 µV/m and 6 pT. The assumption of an infinite source scale overestimates the ionospheric response by a factor of ∼7 as compared with realistic scale 60 km of the ZEVS transmitter. Unbalanced 50 Hz current of 10 A in large‐scale (>100 km) power transmission lines can produce the electric response in the upper ionosphere that is sufficient to be detected by electric sensors at LEO satellite. The stimulation of artificial Pc1 pulsations (0.5 Hz) with amplitudes ∼1 pT and ∼10 µV/m by large‐scale (>100 km) power lines is possible with driving current >100 A. The use of decommissioned power lines can be a cheap and efficient tool to stimulate Pc1 pulsations in the ionosphere.

Addressing erroneous scale assumptions in microbe and gene set enrichment analysis.

By applying Differential Set Analysis (DSA) to sequence count data, researchers can determine whether groups of microbes or genes are differentially enriched. Yet sequence count data suffer from a scale limitation: these data lack information about the scale (i.e., size) of the biological system under study, leading some authors to call these data compositional (i.e., proportional). In this article, we show that commonly used DSA methods that rely on normalization make strong, implicit assumptions about the unmeasured system scale. We show that even small errors in these scale assumptions can lead to positive predictive values as low as 9%. To address this problem, we take three novel approaches. First, we introduce a sensitivity analysis framework to identify when modeling results are robust to such errors and when they are suspect. Unlike standard benchmarking studies, this framework does not require ground-truth knowledge and can therefore be applied to both simulated and real data. Second, we introduce a statistical test that provably controls Type-I error at a nominal rate despite errors in scale assumptions. Finally, we discuss how the impact of scale limitations depends on a researcher's scientific goals and provide tools that researchers can use to evaluate whether their goals are at risk from erroneous scale assumptions. Overall, the goal of this article is to catalyze future research into the impact of scale limitations in analyses of sequence count data; to illustrate that scale limitations can lead to inferential errors in practice; yet to also show that rigorous and reproducible scale reliant inference is possible if done carefully.

Mapping surface water dynamics (1985–2021) in the Hudson Bay Lowlands, Canada using sub-pixel Landsat analysis

The fate of the carbon stored in frozen peatlands in Canada's Hudson Bay Lowlands (HBL) depends strongly on water, with wetter conditions favoring long-term storage. Dynamic surface water products generated from historical Landsat data exist to inform surface water trends in the HBL based on binary classifications of land vs water at 30 m spatial resolution. However, the HBL contains many water features smaller than 30 m, including streams and patterned fens that require a sub-pixel mapping approach to fully capture their dynamics. In this paper, we leverage an existing binary dynamic surface water product to generate a spatially and temporally comprehensive Landsat sub-pixel surface water time-series over the HBL. We first generate Landsat Red, NIR and SWIR composites from 1985 to 2021 and evaluate data-driven machine learning and physical models to derive sub-30 m water fractions across the entire mapping domain. Data-driven models were calibrated on 30 m water fractions obtained from 16 of 17 WorldView scene water fraction maps and assessed on the 17th held-out scene in a jackknife validation. Data-driven models were also calibrated by relating scaled Landsat reflectance to water fractions obtained from binary water masks at corresponding scales from 90 to 270 m. Physical models involved simple linear unmixing using a new approach that samples land endmembers in the vicinity of each pixel to represent land reflectance, and a global water endmember sampled beneath permanent water in each image. The assumption of linear scaling was verified at sub-30 m to 270 m resolution for NIR, SWIR and NDVI, which were all highly correlated with water fraction and had no significant differences among water fraction – spectral feature relationships across the full range of scales. Each of 11 different methods and input spectral features were evaluated against WorldView water fractions and ranked based on nine criteria. We found that machine learning using all spectral features including local NIR land endmembers performed best among data-driven approaches, and linear unmixing of the NIR band using local land endmembers performed best among physical. Both best-performing methods were applied to the entire time-series and surface water area trends were calculated and compared with trends obtained from binary water masks. All three methods agree on the direction of surface water change towards wetting, with sub-pixel inter-annual variation agreeing with stream discharge noted in other studies.

Modified DFA for a robust discrimination between short-term and long-range correlations in short time series

Since the standard detrended fluctuation analysis (s-DFA) method depends on asymptotic power-law scaling assumption, it has been questioned on its ability in characterizing the correlation structure at the small scales, let alone discriminating the correlation structures of short time series. A modified DFA (m-DFA) with a novel defined fluctuation function is employed in this study to discriminate and characterize the distinct (short-termed or long-ranged) correlation structures in short time series. Detailed results show that the m-DFA is able not only to distinguish the short-termed, or long-ranged correlation, but also to well quantify the correlation strengths in both output from classical models and real-world series (for example, DTR variability over China) of data length as short as 2000. Moreover, m-DFA can work effectively in time series with strong correlation of even shorter length as 500. The correlation structures inferred by m-DFA in short intervals contribute greatly to better understanding of local and evolutionary correlation features of an underlying process, not limited to only global one from s-DFA.

Efficiency of subnational government expenditure towards elementary education and nutrition: Bootstrap data envelopment analysis for India

The need of translating increasing outlays into better outcomes on various public programmes has attracted the attention of researchers worldwide to focus more on the quality of public spending, often assessed in terms of its efficiency. The present article is a contribution to the existing literature on the subject in that it assesses the efficiency of government expenditure of Indian states for two most basic social services—elementary education and nutrition during 2014–2015 and 2018–2019 using data envelopment analysis and Malmquist productivity index techniques, in both input‐oriented as well as output‐oriented settings under variable returns to scale assumption; it constructs the average performance index for children at elementary education and malnutrition index for women and children to utilise them as output indicators; and it adopts a robust bootstrap truncated regression procedure to avoid various econometric issues while estimating the impact of selected environmental factors on bias‐corrected inefficiency scores. The major findings of this article seem to suggest that, while states should be provided greater flexibility in their fiscal operations, they have to complement their fiscal autonomy with good governance to improve the efficiency of their spending on basic social services. Towards this end, states like Bihar, Jharkhand and those belonging to North‐Eastern and Himalayan regions need special attention with a different set of development policies.

The impact of climate change on economic growth: Evidence from a panel of Asian countries

Asia is recognized as one of the most vulnerable regions. This research aims to identify climate change effects on economic growth. It proposes a new and comprehensive perspective to examine the climate-economy nexus in this region and provides an underpinning for assessing the pathway of the growing Asian economy under the SSP climate scenario (CMIP6). We apply a macroeconomic-climate modeling approach with a climate damage function. The damage function, which is based on the temperature anomaly, was examined under three classes of damage severity. The climate change effect has been examined by including the direct effect on the output as the level effect and two more channels, including capital depreciation and productivity growth reduction. The augmented Solow growth model framework that considers different types of capital, including physical, human, social, and environmental capital, was applied. The labor productivity or technology is assumed to depend on trade-related variables, including trade openness, financial development, and foreign aid inflows. Also, in order to test the constant returns to scale assumption, the CES production function, which is the flexible production technology, was used. The study relied on the country-year panel of GDP per capita and other macroeconomic variables such as labor force, capital formation, financial development index, trade openness, and foreign aid gleaned for 1994–2017 to estimate production functions using the GMM estimation method. The climate data on the annual mean temperature and projections of future temperature are based on ICMP6 by 2100 for Asian countries. Based on the CES estimation results, constant returns to scale or Cobb-Douglas production function was adopted. The estimation results show that physical and environmental capital account for the highest contribution to the output per worker. However, the contribution of trade-related variables was found to be insignificant. The projected pathway by 2100 establishes that climate change would significantly reduce Asian output per worker, especially if severe damage function is examined, and climate change stays on the SSP scenario-anticipated trajectory. The output elasticity with respect to temperature under the most severe scenario was obtained −22.80, corresponding to the output per worker reduction of 46.7 percent in 2100. Among the three channels of the climate effect, productivity growth reduction showed the most adverse effect on output. The lower flexibility of the production function that restricts the environmental replacement with other inputs, may lead to a more binding role under growing scarcity conditions. It was also found that labor and technology could contribute dampening the capital damage induced by higher temperatures. From the research results, the findings suggest measures aiming at providing flexible production technology, development of capital-embodied technologies, and lower dependence on environmental capital.

A generalized closed-form solution for 3D registration of two-point sets under isotropic and anisotropic scaling

Fitting of two-point sets under non-uniform scaling involves several applications, including ultrasound-guided surgery, where ultrasound images generally show anisotropy between its lateral and depth resolution. However, the current state-of-the-art only accomplishes the closed-form solution under the assumption of isotropic scaling, and only the iterative form of the solution is available for registration regardless of scaling type. A generalized closed-form solution, including anisotropic scaling, could robust the computation in the applications of multi-modality image fusion and surgical navigation based on ultrasound images. In this paper, a generalized closed-form solution (GCFS) that accounts for isotropic scaling and anisotropic scaling is proposed. GCFS finds the least-squares solution of rotation, translation, and scaling based on the singular value decomposition (SVD). The method was demonstrated to 1) register two 3D point sets under the effect of anisotropic scaling and 2) register two coplanar 3D point sets under the effect of anisotropic scaling. This study evaluates 3D registration between the preoperative model and intraoperative ultrasonic scanning of a femur and 2D registration of ultrasound images to the phantom for ultrasound calibration. In addition, the conditions that affect the transformation estimations like estimating reflection and noise degeneracy were also considered in the evaluation.

A deep learning factor analysis model based on importance‐weighted variational inference and normalizing flow priors: Evaluation within a set of multidimensional performance assessments in youth elite soccer players

AbstractExploratory factor analysis is a widely used framework in the social and behavioral sciences. Since measurement errors are always present in human behavior data, latent factors, generating the observed data, are important to identify. While most factor analysis methods rely on linear relationships in the data‐generating process, deep learning models can provide more flexible modeling approaches. However, two problems need to be addressed. First, for interpretation, scaling assumptions are required, which can be (at least) cumbersome for deep generative models. Second, deep generative models are typically not identifiable, which is required in order to identify the underlying latent constructs. We developed a model that uses a variational autoencoder as an estimator for a complex factor analysis model based on importance‐weighted variational inference. In order to receive interpretable results and an identified model, we use a linear factor model with identification constraints in the measurement model. To maintain the flexibility of the model, we use normalizing flow latent priors. Within the evaluation of performance measures in a talent development program in soccer, we found more clarity in the separation of the identified underlying latent dimensions with our models compared to traditional PCA analyses.