Empirical Frequency Research Articles

Characterizing selection on complex traits through conditional frequency spectra.

Natural selection on complex traits is difficult to study in part due to the ascertainment inherent to genome-wide association studies (GWAS). The power to detect a trait-associated variant in GWAS is a function of frequency and effect size - but for traits under selection, the effect size of a variant determines the strength of selection against it, constraining its frequency. Recognizing the biases inherent to GWAS ascertainment, we propose studying the joint distribution of allele frequencies across populations, conditional on the frequencies in the GWAS cohort. Before considering these conditional frequency spectra, we first characterized the impact of selection and non-equilibrium demography on allele frequency dynamics forwards and backwards in time. We then used these results to understand conditional frequency spectra under realistic human demography. Finally, we investigated empirical conditional frequency spectra for GWAS variants associated with 106 complex traits, finding compelling evidence for either stabilizing or purifying selection. Our results provide insight into polygenic score portability and other properties of variants ascertained with GWAS, highlighting the utility of conditional frequency spectra.

Phylogenetic tree instability after taxon addition: empirical frequency, predictability, and consequences for online inference.

Online phylogenetic inference methods add sequentially arriving sequences to an inferred phylogeny without the need to recompute the entire tree from scratch. Some online method implementations exist already, but there remains concern that additional sequences may change the topological relationship among the original set of taxa. We call such a change in tree topology a lack of stability for the inferred tree. In this paper, we analyze the stability of single taxon addition in a Maximum Likelihood framework across 1, 000 empirical datasets. We find that instability occurs in almost 90% of our examples, although observed topological differences do not always reach significance under the AU-test. Changes in tree topology after addition of a taxon rarely occur close to its attachment location, and are more frequently observed in more distant tree locations carrying low bootstrap support. To investigate whether instability is predictable, we hypothesize sources of instability and design summary statistics addressing these hypotheses. Using these summary statistics as input features for machine learning under random forests, we are able to predict instability and can identify the most influential features. In summary, it does not appear that a strict insertion-only online inference method will deliver globally optimal trees, although relaxing insertion strictness by allowing for a small number of final tree rearrangements or accepting slightly suboptimal solutions appears feasible.

A Probabilistic Statistical Risk Assessment Method for Soil Erosion Using Remote Sensing Data: A Case Study of the Dali River Basin

Soil erosion risk assessment enables the identification of areas requiring priority treatment and avoids wasting human and material resources. The factor scoring method used in existing studies has high subjectivity, and the method of expressing erosion risk according to the soil erosion intensity ignores the random nature of the occurrence of erosion; therefore, neither method accurately reflects the risk of soil erosion. In order to address this issue, this study proposes a soil erosion risk assessment method that integrates the outcome and the probability of occurrence of soil erosion by means of a probabilistic statistical model. Subsequently, experimental research is conducted in the Dali River Basin. On the basis of long time-series data, using mathematical statistics as a tool and drawing on the empirical frequency formula, the probabilistic statistical risk assessment model is combined with the Modified Universal Soil Loss Equation (RUSLE) model to account for the probability of regional soil erosion at different intensity levels in the long time-series, which is combined with the intensity of erosion to carry out soil erosion risk assessment. The results of our study show the following: (1) The central and southwestern regions of the Dali River Basin (DRB) present medium and high levels of soil erosion risk, with the proportion of low-risk areas increasing annually, accounting for 78.97% of the DRB in 2020, while extremely high-risk areas account for only 0.40% of the DRB. (2) The major components impacting soil erosion risk in the DRB, as revealed by the geodetector, are the normalized difference vegetation index (NDVI) and slope, where the interaction between the two dominated the spatial variation in soil erosion risk. (3) Comparing the soil erosion risk and its status in the coming years, the proposed assessment method based on the occurrence probability can reveal the future soil erosion risk better than the traditional assessment method.

Modifiable Risk Factors Related to Oral Diseases in Youth Cuban Baseball Sportsmen

Background Oral health care closes the cycle of medical assistance integrated with sports, becoming a specialized service of great value in Cuba; however, oral diseases in young athletes are very frequent. For effective prevention, it is necessary to know the modifiable risk factors related to these diseases. Objective This study aimed to determine the relationship between risk factors and oral diseases in baseball sportsmen from the sports initiation school of Villa Clara, Cuba. Material and Methods A descriptive, correlational, and cross-sectional study was carried out in the young baseball athletes (N=60) of the 15U (n=30) and 18U (n=30) divisions (M=15.33; SD=1.49). Data were analyzed using empirical frequency distribution and descriptive statistics. Data normality was tested using asymmetry, kurtosis, and the Kolmogorov-Smirnov test. Mann-Whitney U test was used to determine differences in the risk factors and oral diseases between divisions, and the Tau_b Kendall correlation coefficient was used to determine relationships between both groups of variables. Results Improper tooth brushing, cariogenic diet, and inefficient oral hygiene were the main risk factors, while dental caries, gingivitis, and malocclusions were the oral diseases most notable. Athletes of higher division have greater toxic habits and a cariogenic diet; however, they brush more frequently and have more efficient oral hygiene. Except for the presence of malocclusions, the rest of the conditions are related to the determined risk factors. Conclusion The knowledge about the relationship between risk factors and oral conditions allows to base the design of educational intervention actions focused on the promotion of adequate oral health behaviors in the athletes, which shows the relevance of odontology in sports.

Adaptive spectrum amplitude modulation method for rolling bearing fault frequency determination

Abstract Signal preprocessing and feature extraction are decisive factors in determining the frequency of bearing faults. The presence of noise interference in the status signal of rolling bearings often hampers accurate fault detection. Although there are various methods for preprocessing vibration signals in rolling bearings, they need further improvement in terms of enhancing fault feature expression and localizing fault frequency bands. This limitation significantly hinders the accuracy of fault frequency determination. In order to enhance the representation of fault information on the frequency spectrum, this study proposes a combined approach that incorporates sparse stacked autoencoder (SSAE), wavelet packet decomposition (WPD), and adaptive spectrum amplitude modulation (ASAM). The resulting method is referred to as SSAE-WPD-ASAM. Firstly, the bearing vibration signal is decomposed by wavelet packet according to the scale and frequency band of the signal. On this basis, the signal reconstruction is realized based on the wavelet packet coefficient and energy distribution in different frequency bands. Secondly, for the whole life cycle signal, the reconstructed signal is self-encoded by sparse stacked autoencoder to achieve dimensionality reduction of the reconstructed signal. Then, the spare reconstructed signal is subjected to ASAM. Finally, through envelope demodulation, peak detection of fault frequency and empirical fault frequency comparison, the specific fault types of rolling bearings are determined. The proposed method is verified by theoretical simulation and three groups of practical experiments. The results show that the proposed method has a significant improvement in diagnostic efficiency and accuracy compared with traditional diagnostic methods.

Taking a Chance in the Classroom: Puzzling Probabilities of Probability Puzzles

Puzzles are an entertaining way to teach probability. But for certain puzzles often the solution probabilities are incorrect. Probability calculations require probability distributions. When the puzzle does not include this information, probabilities claiming to be the unconditional correct answer are incorrect. The probability of an outcome of a past event is either 1 when the outcome is favorable or 0 when it is not. Puzzles that ask for the probability of a past event’s outcome and give the probability of that outcome before the event occurs are incorrect. Various classical puzzles commit these errors using axiomatic, relative frequency, or empirical frequency probability. There are simple ways to resolve these errors. Twelve lessons are provided to avoid misteaching and incorrect answers.

Conditional frequency spectra as a tool for studying selection on complex traits in biobanks.

Natural selection on complex traits is difficult to study in part due to the ascertainment inherent to genome-wide association studies (GWAS). The power to detect a trait-associated variant in GWAS is a function of frequency and effect size - but for traits under selection, the effect size of a variant determines the strength of selection against it, constraining its frequency. To account for GWAS ascertainment, we propose studying the joint distribution of allele frequencies across populations, conditional on the frequencies in the GWAS cohort. Before considering these conditional frequency spectra, we first characterized the impact of selection and non-equilibrium demography on allele frequency dynamics forwards and backwards in time. We then used these results to understand conditional frequency spectra under realistic human demography. Finally, we investigated empirical conditional frequency spectra for GWAS variants associated with 106 complex traits, finding compelling evidence for either stabilizing or purifying selection. Our results provide insight into polygenic score portability and other properties of variants ascertained with GWAS, highlighting the utility of conditional frequency spectra.

Dual-frame optimization for informationally complete quantum measurements

Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of positive operator-valued measure (POVM) effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the postprocessing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox. Published by the American Physical Society 2024

The Patterns of Codon Usage between Chordates and Arthropods are Different but Co-evolving with Mutational Biases.

Different frequencies amongst codons that encode the same amino acid (i.e. synonymous codons) have been observed in multiple species. Studies focused on uncovering the forces that drive such codon usage showed that a combined effect of mutational biases and translational selection works to produce different frequencies of synonymous codons. However, only few have been able to measure and distinguish between these forces that may leave similar traces on the coding regions. Here, we have developed a codon model that allows the disentangling of mutation, selection on amino acids and synonymous codons, and GC-biased gene conversion (gBGC) which we employed on an extensive dataset of 415 chordates and 191 arthropods. We found that chordates need 15 more synonymous codon categories than arthropods to explain the empirical codon frequencies, which suggests that the extent of codon usage can vary greatly between animal phyla. Moreover, methylation at CpG sites seems to partially explain these patterns of codon usage in chordates but not in arthropods. Despite the differences between the two phyla, our findings demonstrate that in both, GC-rich codons are disfavored when mutations are GC-biased, and the opposite is true when mutations are AT-biased. This indicates that selection on the genomic coding regions might act primarily to stabilize its GC/AT content on a genome-wide level. Our study shows that the degree of synonymous codon usage varies considerably among animals, but is likely governed by a common underlying dynamic.

The effect of urban environment on large-scale path loss model’s main parameters for mmWave 5G mobile network in Iraq

Abstract The high speeds resulting from the use of millimeter waves (mmWave) in 5G mobile networks are accompanied by high path loss. The issue of generating a reliable propagation model of radio waves is crucial to the development of cellular networks since it reveals essential information regarding the properties of the wireless channel. The received signal strength, the coverage area, and the outage probability in certain places may all be determined through theoretical or empirical radio frequency propagation models, which offer essential valuable information regarding signal path loss and fading. This work analyzes a comprehensive three-dimensional ray-tracing method at 28 GHz for Najaf city, Iraq. The optimum path loss model for the city of Najaf is evaluated using the close-in (CI) model. On average, the values of the main parameters of CI model n n , X σ CI {X}_{\sigma }^{{\rm{CI}}} accomplished, respectively, 3.461866667 and 11.13958333. The lowest achievable path loss exponent was 3.0619 across all analyzed scenarios, while the highest possible value was 4.1253. The results of this work can serve as a baseline for mmWave measurement campaigns conducted in comparable conditions, and they provide a new avenue for future research into mmWave at 28 GHz in Iraq.

Frequency-Dependent Contrast Enhancement for Conductive and Non-Conductive Materials in Electrical Impedance Tomography

This research investigates the critical role of frequency selection in Electrical Impedance Tomography (EIT), a non-invasive imaging technique that reconstructs internal conductivity distributions through injected electrical currents. Empirical frequency selection is paramount to maximizing the fidelity and specificity of EIT images. The study explores the impact of distinct frequency ranges—low, medium, and high—on image contrast and clarity, particularly focusing on differentiating conductive materials from non-conductive materials. The findings reveal distinct empirical frequency bands for enhancing the respective contrasts: 15–38 kHz for conductive materials (copper) and 45–75 kHz for non-conductive materials (acrylic resin). These insights shed light on the frequency-dependent nature of material contrast in EIT images, guiding the selection of empirical operating ranges for various target materials. This research paves the way for improved sensitivity and broader applicability of EIT in diverse areas.

Empirical Frequency Content Models for Offshore Ground Motions in the Japan Trench Area

ABSTRACT This paper presents empirical models for the frequency content parameters of offshore ground motions in the Japan Trench area based on the S-net dataset, comprising 6,436 recordings from 496 events. Significant variations in frequency content among shallow crustal, upper-mantle, subduction interface and subducting slab are revealed. Empirical models for To, Tavg, and Tm are proposed, considering moment magnitude, source distance, focal depth, and tectonic types. A comparative analysis with four existing land models highlights differences. Total residual results indicate that land models, based on shallow crustal datasets, tend to overestimate observed frequency content parameters in the Japan Trench area.

Effect of lake waves on manoeuvring performance of a model ship

ABSTRACT In this study, we investigate how natural environmental conditions affect a training vessel using a ‘mathematical model of wind and wave’ specific to Lake Silm near Kamionka, Poland. Wind and wave measurements on the lake were conducted. We present the vessel’s trajectory under varying conditions: navigating in restricted waters simulating port conditions with speed readings, and during propeller operation. The control system of the nonlinear autonomous object employed two controllers: a linear matrix inequality controller and an overriding trajectory controller. We assess the impact of nonlinearities in the measured waves. It is shown that the maximum entropy probability distribution conforms more closely to the empirical frequency histogram than the Gaussian distribution. The wave height probability distributions diverge from Rayleigh distributions, indicating slight nonlinear effects. These results enhance the mathematical model of Silm Lake’s wave dynamics.

Exploring the joint probability of precipitation and soil moisture over Europe using copulas

Abstract. The joint probability of precipitation and soil moisture is here investigated over Europe with the goal to extrapolate meaningful insights into the potential joint use of these variables for the detection of agricultural droughts within a multivariate probabilistic modeling framework. The use of copulas is explored, being the framework often used in hydrological studies for the analysis of bivariate distributions. The analysis is performed for the period 1996–2020 on the empirical frequencies derived from ERA5 precipitation and LISFLOOD soil moisture datasets, both available as part of the Copernicus European Drought Observatory. The results show an overall good correlation between the two standardized series (Kendall's τ= 0.42±0.1) but also clear spatial patterns in the tail dependence derived with both non-parametric and parametric approaches. About half of the domain shows symmetric tail dependence, well reproduced by the Student's t copula, whereas the rest of the domain is almost equally split between low- and high-tail dependences (both modeled with the Gumbel family of copulas). These spatial patterns are reasonably reproduced by a random forest classifier, suggesting that this outcome is not driven by chance. This study stresses how a joint use of standardized precipitation and soil moisture for agriculture drought characterization may be beneficial in areas with strong low-tail dependence and how this behavior should be carefully considered in multivariate drought studies.

A Subject-Specific Attention Index Based on the Weighted Spectral Power.

As an essential cognitive function, attention has been widely studied and various indices based on EEG have been proposed for its convenience and easy availability for real-time attention monitoring. Although existing indices based on spectral power of empirical frequency bands are able to describe the attentional state in some way, the reliability still needs to be improved. This paper proposed a subject-specific attention index based on the weighted spectral power. Unlike traditional indices, the ranges of frequency bands are not empirical but obtained from subject-specific change patterns of spectral power of electroencephalograph (EEG) to overcome the great inter-subject variance. In addition, the contribution of each frequency component in the frequency band is considered different. Specifically, the ratio of power spectral density (PSD) function in attentional and inattentional state is utilized to calculate the weight to enhance the effectiveness of the proposed index. The proposed subject-specific attention index based on the weighted spectral power is evaluated on two open datasets including EEG data of a total of 44 subjects. The results of the proposed index are compared with 3 traditional attention indices using various statistical analysis methods including significance tests and distribution variance measurements. According to the experimental results, the proposed index can describe the attentional state more accurately. The proposed index respectively achieves accuracies of 86.21% and 70.00% at the 1% significance level in both the t-test and Wilcoxon rank-sum test for two datasets, which obtains improvements of 41.38% and 20.00% compared to the best result of the traditional indices. These results indicate that the proposed index provides an efficient way to measure attentional state.

Investigation of Feature Engineering Methods for Domain-Knowledge-Assisted Bearing Fault Diagnosis.

The engineering challenge of rolling bearing condition monitoring has led to a large number of method developments over the past few years. Most commonly, vibration measurement data are used for fault diagnosis using machine learning algorithms. In current research, purely data-driven deep learning methods are becoming increasingly popular, aiming for accurate predictions of bearing faults without requiring bearing-specific domain knowledge. Opposing this trend in popularity, the present paper takes a more traditional approach, incorporating domain knowledge by evaluating a variety of feature engineering methods in combination with a random forest classifier. For a comprehensive feature engineering study, a total of 42 mathematical feature formulas are combined with the preprocessing methods of envelope analysis, empirical mode decomposition, wavelet transforms, and frequency band separations. While each single processing method and feature formula is known from the literature, the presented paper contributes to the body of knowledge by investigating novel series connections of processing methods and feature formulas. Using the CWRU bearing fault data for performance evaluation, feature calculation based on the processing method of frequency band separation leads to particularly high prediction accuracies, while at the same time being very efficient in terms of low computational effort. Additionally, in comparison with deep learning approaches, the proposed feature engineering method provides excellent accuracies and enables explainability.

Dynamic modelling of price expectations and judgments

Official data about consumers’ qualitative expectation and perception of inflation are derived from repeated surveys conducted by national statistical institutes. In EU, these data are published in aggregate form, and cannot be described by means of classical methods based on cumulative models for ordinal data. This article illustrates an integrated approach that locates CUB mixture models for ratings in a time series perspective in order to investigate the joint evolution of inflation judgments and expectations in Italy. In order to measure the common sentiment of interviewees through the feeling component of the model, net of possible uncertainty and nuisance effects, its estimation is pursued through profile likelihood methods given the empirical frequency distributions of consumers’ opinions observed over time. Then, the relationship between the time series of the estimated feeling parameters is modelled using a dynamic regression model and the results are compared in three periods marked by different economic conditions. Results indicate that each series has a substantial inertial component, and thus it is characterized by a slow variation over time, and that both judgments about past price levels and previous expectations affect current expectations about the future in fairly different ways for the three time periods.

A New Model for Solving Hydrological Connectivity Inside Soils by Fast Field Cycling NMR Relaxometry

In this paper, a new quantitative approach for estimating the structural and functional connectivity inside soil by Fast Field Cycling (FFC) NMR relaxometry is presented, tested by measurements carried out in three samples with different texture characteristics. Measurements by FFC NMR relaxometry have been carried out using water-suspended samples and Proton Larmor frequencies (νL) ranging in the 0.015–35 MHz interval. Two non-degraded soil samples, with different textural characteristics, and a degraded soil collected in a badland area, were analyzed. For a given soil and any applied Proton Larmor frequency, the distribution of the longitudinal relaxation times, T1, (i.e., relaxogram) measured by FFC NMR has been integrated, and the resulting S-shaped curve (i.e., relaxogram integration curve) was represented, for the first time, by Gumbel’s diagram. This new representation of the relaxogram integration curve, transforming the S-shaped curve into a straight line, allowed for distinguishing three linear components, corresponding to three different relaxation time ranges, characterized by three different slopes. Two points, identified by the abrupt slope changes of the relaxogram integration curve plotted in Gumbel’s diagram, are used to identify two characteristic values of relaxation time, T1A and T1B, which define three well-known pore size classes (T1 < T1A micro-pores, T1A < T1 < T1B meso-pores, and T1 > T1B macro-pores). The relaxogram integration curve allowed for calculating the non-exceeding empirical cumulative frequency, F(T1), corresponding to the characteristic T1A and T1B values. The analysis demonstrated that the relaxogram can be used to determine the pore-size ranges of each investigated sample. Finally, using the slope values of the three components of the relaxogram integration curve, a new definition of the Structural Connectivity Index, SCI, and Functional Connectivity Index, FCI, was proposed.

Data-driven analysis for disturbance amplification in car-following behavior of automated vehicles

This paper presents a data-driven framework to quantitatively analyze the disturbance amplification behavior of automated vehicles in car-following (CF). The data-driven framework can be applied to unknown CF controllers based on the concept of empirical frequency response function (FRF). Specifically, a well-known signal processing method, Welch's method, together with a short time Fourier transformation is developed to extract the empirical transfer functions from vehicle trajectories. The method is first developed assuming a generic linear controller with time-invariant CF control features (e.g., control gains) and later extended to capture time-variant features. The proposed methods are evaluated for estimation consistencies via synthetic data-based simulations. The evaluation includes the performances of the linear approximation accuracy for a linear time-invariant controller, a nonlinear controller, and a linear time-variant controller. Results indicate that our framework can provide reasonably consistent results as theoretical ones in terms of disturbance amplification. Further it can perform better than a linear theoretical analysis of disturbance amplification, particularly when nonlinearity in CF behavior is present. The methods are applied to existing field data collected from vehicles with adaptive cruise control (ACC) on the market. Findings reveal that all tested vehicles tend to amplify disturbances, particularly in low frequency (< 0.5 Hz). Further, the results demonstrate that these ACC vehicles exhibit time-varying features in terms of disturbance amplification ratio depending on the leading vehicle trajectories.

Paradoxes of MaxEnt markedness

Over the past two decades, theoretical linguistics has taken a probabilistic turn. Maximum entropy (ME) has been endorsed as a model of probabilistic phonology because of its classical guarantees for grammatical inference. Yet, little is known about the basic organizing principles of ME phonology beyond circumstantial evidence of ME’s ability to fit specific patterns of empirical frequencies. The study of ME typologies is difficult because they consist of infinitely many grammars that cannot be exhaustively listed and directly inspected. Uniform Probability Inequalities (Anttila and Magri 2018) are a new tool that solves the problem: they characterize cases where one phonological mapping has a probability smaller than another mapping and this probability inequality holds uniformly for every grammar in the typology. In other words, uniform probability inequalities are universals of probabilistic grammars. We present a new generalization about ME uniform probability inequalities and argue that they are phonologically paradoxical and prune the set of ME universals down to almost nothing. This suggests that ME is not a suitable model of phonology.