Hypothetical Distribution Research Articles

Probability density prediction for carbon allowance prices based on TS2Vec and distribution Transformer

Carbon allowance price is an important tool to reduce carbon emissions and achieve carbon neutrality. It is necessary to establish a predictive model to provide accurate and reliable information to managers and participants in the carbon trading market. Therefore, a novel probability density prediction model, called TS2Vec-based distribution Transformer (TDT), is proposed. TDT consists of two stages: contrastive unsupervised pre-training and supervised training. In the contrastive unsupervised training stage, time series to vector (TS2Vec) is used to represent the dynamic trends and unique features of the data. Then, these representations are fed into the distribution Transformer (DT) to fit the hypothetical probability distribution. Experimental results show that the prediction results of the proposed TDT are more accurate and reliable than other benchmark models. In addition, our research indicates reliable probability density predictions provide enterprises with opportunities to control carbon emission costs and increase economic returns, thereby improving the competitiveness of enterprises and promoting carbon emission reduction.

Estimating the impact of social distance policy in mitigating COVID-19 spread with factor-based imputation approach

AbstractWe identify the effectiveness of social distancing policies in reducing the transmission of the COVID-19 spread. We build a model that measures the relative frequency and geographic distribution of the virus growth rate and provides hypothetical infection distribution in the states that enacted the social distancing policies, where we control time-varying, observed and unobserved, state-level heterogeneities. Using panel data on infection and deaths in all US states from February 20 to April 20, 2020, we find that stay-at-home orders and other types of social distancing policies significantly reduced the growth rate of infection and deaths. We show that the effects are time varying and range from the weakest at the beginning of policy intervention to the strongest by the end of our sample period. We also found that social distancing policies were more effective in states with higher income, better education, more white people, more democratic voters, and higher CNN viewership.

Remaining Useful Life for Heavy-Duty Railway Cast Steel Knuckles Based on Crack Growth Behavior with Hypothetical Distributions

The current research on the integrity of critical structures of rail vehicles mainly focuses on the design stage, which needs an effective method for assessing the service state. This paper proposes a framework for predicting the remaining useful life (RUL) of in-service structures with and without visible cracks. The hypothetical distribution and delay time models were used to apply the equivalent crack growth life data of heavy-duty railway cast steel knuckles, which revealed the evolution characteristics of the crack length and life scores of the knuckle under different fracture failure modes. The results indicate that the method effectively predicts the RUL of service knuckles in different failure modes based on the cumulative failure probability curves for different locations and surface crack lengths. This study proposes an RUL prediction framework that supports the dynamic overhaul and state maintenance of knuckle fatigue cracks.

Biometric description of 34 589 eyes undergoing cataract surgery: sex differences.

To describe gender differences in the biometric parameters of a large sample of patients with cataract. Cataract surgery has evolved from a vision restoration to a refractive procedure, and population-based studies are vital to optimize normative databases and postsurgical outcomes. Miguel Servet University Hospital, Zaragoza, Spain. Retrospective single-center observational study. The study included 34 589 eyes (20 004 patients with cataract). Biometric data were obtained from IOL Master 700 and Pentacam HR. Linear mixed models were used to account for intereye correlation. HofferQST formula was used to calculate the hypothetical distribution of intraocular lens (IOL) power (arbitrary lens; A = 119.2). Most biometric variables showed significant differences between sexes ( P < .0001), such as 0.53 mm shorter eyes found in females, of which 0.16 mm are explained by shorter aqueous depth. Steeper anterior keratometries (∼0.75 diopter [D]) were found in women, to end up in no difference on anterior astigmatism magnitude, but different orientation ( P < .0001). The distribution of IOL power differed between sexes ( P < .001), with the interquartile range shifting 1 D toward more powerful lenses in women and odds ratio (power >26 D) = 2.26, P < .0001 (Fisher). Large sample size studies provide smaller margin of error, higher power, and controlled risk of reporting false (negative or positive) findings. Highly significant differences between sexes in ocular biometry were found; this supports the idea that including sex as a parameter in IOL calculation should be explored and may improve results. In addition, the distribution of IOL powers was provided, which may be useful for manufacturers and hospital stock planning.

Long-term trend and variability in surface temperatures over Emilia-Romagna from 1962 to 2022

Scientific interest is increasingly drawn towards regional meteorological extremes, given their impacts on populations, infrastructure, and ecosystems. These extremes are shaped by complex interactions between internal climate variability and long-term trends. The aim of the present work is to evaluate changes in high-frequency variability and the influence of long-term trends on the frequency of occurrences of extremes, with a focus on surface temperatures over the period from 1962 to 2022 in Emilia-Romagna, a region of Northern Italy. Daily data of 2 m air temperatures averaged over the region are retrieved from ERACLITO, a high-resolution climate analysis. The distributions of daily temperature anomalies show a general broadening in 1992–2022 with respect to 1962–1991. This is true for maximum, minimum, and mean daily surface temperatures, especially during the summer and spring seasons. A significant warming trend of 0.37 °C/decade is detected in annual mean surface temperatures over the period considered. The study is completed with a comparison between the observed frequency of record-breaking annual temperature events, a hypothetical stationary climate distribution and a theoretical derivation that accounts for changes in trends and variability. During the last decade, the theoretical count of extreme events is 1.26, which yields a likelihood of 86% that this is owed to the trend rather than interannual variability. Idealized experiments demonstrate that the expected occurrences of record-breaking events in future decades depend on the warming rate rather than the warming level. Finally, an analysis performed at seasonal level shows that the majority (minority) of record events are occurring in the summer (spring) seasons.

Rotated Lorenz Curves of Biological Size Distributions Follow Two Performance Equations

The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2, a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well.

Impact on backpropagation of the spatial heterogeneity of sodium channel kinetics in the axon initial segment.

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (NaVs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of NaVs with gating properties that are "right-shifted" to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of NaV subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of NaV subtypes in the AIS. We implemented a range of hypothetical NaV distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of NaV subtypes is varied. With axonal stimulation, proximal NaV availability dominates, such that concentrating right-shifted NaVs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted NaVs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of NaV1.2 and NaV1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these NaV subtypes.

Proposal of a West-High–East-Low Hypothetical Theory forthe Longitudinal Distribution of Global Height

In this study, we seek to propose a hypothetical theory of western high-east low and the K&amp;F theory (Kani and Fujii theory), similar to Bergmann's law of north-high and south-low for height, as laws based on latitude and longitude with regard to the trends in global height distribution. Judging from the changes in height over the 100-year span from 1870 to 1970, a composition was suggested in which, taking the European region as the center, height was clearly higher in the west and lower in the east with eastward movement. In other words, it was speculated that diversity decreased as people moved east, leading to slower economic development, lower wealth, and shorter stature. Therefore, we can hypothesize a west-high, east-low composition in the height distribution over longitude. Here, we propose the K&amp;F theory (Kani and Fujii theory) to explain the hypothetical theory of west-high, east-low.

Stochastic energy management of a multi-microgrid system with battery/ supercapacitor energy storages considering demand response and transactive energy

This paper proposes stochastic energy management for an electrical system consisting of a multi-microgrid and a distribution company (DISCO). The objective function aims at finding an optimal day-ahead energy schedule of dispatchable resources, energy storages, and demand response in the presence of intermittent renewable energy sources. Two different energy storage devices, i.e., battery and supercapacitor (SC), are modeled in the system to provide both high power and energy density. Wind speed, solar irradiation, and electrical demand uncertainties have been modeled using probability density functions of uncertain parameters, and the number of scenarios has been decreased using mixed-integer linear programming (MILP) based scenario reduction with a novel characteristic. In the proposed model, the DISCO, as a leader, attempts to maximize its profit while the microgrids (MGs), as followers, tend to minimize their operational costs. Karush-Kuhn-Tucker, strong duality, and Fortuny-Amat transformation are used to convert the non-linear bi-level problem into a linear single-level problem. The proposed model was tested on a hypothetical distribution system and the results showed the efficiency of the model in reducing operational costs of MGs by 7.5%, increasing the DISCO profit by 6.9%, and improving the reliability of the system by reducing the energy not supplied.

Growth rate of spherical voids with non-comoving dark matter and baryons

We present numerical solutions to Einstein’s equations describing large spherical cosmic voids constituted by two components: dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous background compatible with the ΛCDM concordance model. We compute numerically the evolution of such configurations in the dark matter frame, with a hypothetical homogeneous distribution of baryons, but respecting the values dictated by the concordance model for the average baryon-to-dark matter density ratio. We reproduce the well-known formation of overdensities at the edge of the void and recover the Lemaître–Tolman–Bondi solutions in the comoving limit of our simulations. We compute the average growth factor of matter fluctuations and find that it departs significantly from the linear perturbative prescription even in the comoving case, where the non-linearity of inhomogeneities has an impact.

The diversity and distribution of Gecarcinidae MacLeay, 1838 (Crustacea: Decapoda: Brachyura), a potential land crab as a valuable food resource, in Indonesia

Gecarcinidae is one of the land crabs that is commonly found in intertidal and coastal areas comprises of 28 species worldwide. On some regions, this crab has been known as one of food resources. However, Indonesians have no interest yet in consuming this potentially high-value species. The present study aims to reveal the diversity and distribution of Gecarcinidae in Indonesia and discuss its potencies. Specimens of Gecarcinidae deposited in Museum Zoologicum Bogoriense (MZB) were used for observation and their morphological differences were recorded. Their recorded localities were used to define the hypothetical distribution. Their economic potential assessments were based on some literatures. In total, there are five species recorded in Indonesia, i.e., Cardisoma carnifex, Gecarcoidea humei, Gecarcoidea lalandii Tuerkayana hirtipes, and Tuerkayana magnum. The widest-distributed species are Cardisoma carnifex and Tuerkayana hirtipes. Among these species, the two largest species are Cardisoma carnifex and Tuerkayana magnum. In Pacific regions, Gecarcoidea is harvested as one of food resources. Therefore, these five species have high potency to support food sustainability and revealing the potencies and chance for captivity could serve as a catalyst to elevate community welfare, especially in coastal areas. Conservation on the natural habitat is necessary to maintain the sustainable utilization.

Detection of Pipes Causing Pressure Loss in Water Distribution Networks via Artificial Immune Systems

This paper proposes the optimization model using Artificial Immune Systems, depending on a model calibration, in order to determine worn out pipes with low Hazen-Williams roughness coefficient causing pressure loss in the water distribution networks. The modified Clonal Selection Algorithm, a type of Artificial Immune Systems, was used as a heuristic optimization method. In order to evaluate its performance, the model was implemented to the four-loop hypothetical water distribution network under steady-state conditions. According to the results, the model appeared to be promising in the detection of old pipes causing high pressure losses in the water distribution networks

Predicting the Magnitude of Microsphere Parameters Obtained from Microscopical Examination of Hardened Concrete

Abstract Geometric probability concepts are used to establish a quantitative basis for predicting the magnitude of microscopically determined parameters of polymeric microsphere systems in hardened concretes relative to the actual magnitude of the parameters. Both a hypothetical discrete size distribution and a representative continuous size distribution of the microspheres are considered in the analysis. It is predicted that for a random section through the concrete, the magnitudes of the measured microsphere volume fraction and specific surface relative to the respective actual values would depend on the proportion of the total number of microspheres counted on the section. The lower the proportion of microspheres counted, the lower the ratios of measured-to-actual volume fraction and measured-to-actual specific surface would be. For the test data presented, the proportion of microspheres counted was calculated to have an average value of 0.75. Ratios of predicted-to-actual volume fraction and predicted-to-actual specific surface are compared with the respective measured ratios and found to be quite accurate. When there is a significant spread in the microsphere size distribution and relatively few microspheres are missed during a microscopical examination of a single section of concrete, the measured volume fraction would be higher and the measured specific surface would be lower, relative to the respective actual values. This is because a random section through the concrete has a greater chance of intersecting large microspheres than small ones, with large microspheres having a relatively higher contribution to volume and a relatively lower contribution to specific surface than small microspheres. These findings are relevant for air-entrained concrete as well when measurements obtained by microscopical examination of hardened concrete are compared with air content measured by the pressure method or with air content and specific surface measured by an air void analyzer.

A Timing Yield Model for SRAM Cells at Sub/Near-Threshold Voltages Based on a Compact Drain Current Model

Sub/near-threshold static random-access memory (SRAM) design is crucial for addressing the memory bottleneck in power-constrained applications. However, the high integration density and reliability under process variations demand an accurate estimation of extremely small failure probabilities. To capture such a “rare event” in memory circuits, the time and storage overhead of conventional simulations based on the Monte Carlo (MC) analysis cannot be tolerated. On the other hand, classic analytical methods predicting failure probabilities from a physical expression become inaccurate in the sub/near-threshold voltage domain due to the hypothetical distribution or the oversimplified drain current ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{ds}$ </tex-math></inline-formula> ) model for nanoscale devices. This work first proposes a simple but efficient empirical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{ds}$ </tex-math></inline-formula> model to describe the drain-induced barrier lowering (DIBL) effect. Based on that, the probability density functions of the interest metrics in SRAM are derived. Two analytical models are then put forward to evaluate SRAM dynamic stabilities, including the access time failure and the write failure. The proposed models can be extended easily to different types of SRAM with different read/write-assist circuits. The models are validated against MC simulations across different operating voltages and temperatures. The average relative errors at 0.5-V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm{ DD}}$ </tex-math></inline-formula> are only 8.8% for the access-time failure model and 10.4% for the write failure model. The size of the required sample data set is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$43.6\times $ </tex-math></inline-formula> smaller than that of the state-of-the-art method.

NGHIÊN CỨU DAO ĐỘNG CỦA DẦM CẦU TRỤC KHI CÁC THAM SỐ MÔ HÌNH LÀ ĐẠI LƯỢNG NGẪU NHIÊN

According to the stochastic design method, the state functions of the design conditions are often built with the appearance of the input random variables with the hypothetical distribution functions and the random responses obtained from the solution of the computational model. This article investigates dynamic behavior of an overhead crane within the system parameters as random variables. First, the physical modeling and differential equation describing the motion of the crane system are derived using the Lagrange equation. Then, the numerical Newmark-β integral method is applied for characterizing dynamic responses of the crane system. Finally, the dynamic responses of the bridge beam are investigated when assuming the model parameters follow the normal distribution. The obtained results show that the distribution characteristics of the vibration response parameters of the bridge girder depend on the standard deviation of the input parameters and the position of the trolley during the investigation time. Specifically, a standard deviation value of 0.15 can cause an uncertainty ~75 % of displacement at the cross-section in the middle of the girder.

Addressing practical aspects of the nuclear criticality safety evaluations with frequentist statistics

General guidelines for Criticality Safety Evaluations (CSE) and regulatory requirements on the Nuclear Criticality Safety are well established nowadays. However, the expert knowledge is often still required in practice. Such situation is typical for the CSE methodologies grounded on the frequentist statistic inference and involving tolerance limits estimations and hypothesis testing. In this respect, various sensitivity tests are illustrated in the given paper to enhance understanding of the statistical assessments, in application to conventional CSE for Light Water Reactor (LWR) fuel configurations, when relatively small validation samples are generally available. It is further discussed that for rare situations with very small validation data samples, both parametric and non-parametric statistical methods have drawbacks: unreliability of normality tests for the first case and large non-parametric margins historically recommended for the second case. For such specific situations, an additional safety margin named “Normality Margin” is proposed in this work, towards compensation of the lack of knowledge of the underlying hypothetical probability distribution describing the criticality validation results.

Remaining useful life prediction framework for crack propagation with a case study of railway heavy duty coupler condition monitoring

A general Remaining useful life (RUL) framework for predicting crack propagation of mechanical system structures based on limited condition monitoring data was proposed. For states of invisible cracks, a method that considers the common characteristics of the object was proposed by using the crack propagation stage as the delay time, combining statistical distribution and hypothesis testing. Then, for the states of visible cracks, methods based on a hypothetical distribution and support vector regression with the Kalman filter considering the current state and individual degradation characteristics were proposed. Finally, taking the condition monitoring data of the coupler body crack state as a case, the RUL prediction from the whole to the individual differences is achieved. The research results indicate that the framework achieves a competitive effect in RUL of internal crack propagation structures of railway wagons, which have important theoretical and practical value for integrity assessment and reliability life prediction.

Underreporting of Top Incomes and Inequality: A Comparison of Correction Methods using Simulations and Linked Survey and Tax Data

Household surveys do not capture incomes at the top of the distribution well. This yields biased inequality measures. We compare the performance of the reweighting and replacing methods to address top incomes underreporting in surveys using information from tax records. The biggest challenge is that the true threshold above which underreporting occurs is unknown. Relying on simulation, we construct a hypothetical true distribution and a “distorted” distribution that mimics an underreporting pattern found in a novel linked data for Uruguay. Our simulations show that if one chooses a threshold that is not close to the true one, corrected inequality measures may be significantly biased. Interestingly, the bias using the replacing method is less sensitive to the choice of threshold. We approach the threshold selection challenge in practice using the Uruguayan linked data. Our findings are analogous to the simulation exercise. These results, however, should not be considered a general assessment of the two methods.

System Dynamics Modeling of Multi-Channel Supply Chain System: A Hypothetical LPG Distribution with Disloyal Household Customers

The availability of LPG in the community is a sensitive issue. If there is a shortage, it has the potential to cause chaos and inflation. The final consumers, namely households and micro business stalls, will generally be disloyal. They are not tied to one particular store to get the LPG they need. Since the number of tanks in circulation will remain constant, the analysis of LPG availability can be focused on the number of tanks. Continuous simulation method with system dynamics is generally used in system growth analysis. In this paper the method is utilized to model the discrete movement of tanks circulating in the community which in this case is represented in a much smaller system, consisting of filling stations, agents, and stores. The modeling results provide a sufficient picture of how the availability of the tank can be optimized appropriately.

Regional income convergence in Colombia: population, space, and long-run dynamics

We examine the trajectory of regional income dynamics in Colombia. Using data on all 33 Colombian departments from 2000 to 2016, we employ extensions of (spatial) Markov chains, space-time mobility measures, along with a fully weighted version of the distribution analysis approach. By considering these extensions, our analysis enables us to answer questions such as whether the role of spatial context influences the distributional dynamics of Colombian departments, or the magnitude of the moderating effect of department’s population. The inclusion of additional measures such as the asymptotic half-life of convergence provides additional results, informing on how long it would take to reach the hypothetical long-run distribution of per capita income. Results, which are reported for both pre- and post-2008 trends, complement previous literature on regional economic convergence in a relevant South American context, showing stronger convergence patterns when controlling for the population living in each department. The patterns do not particularly intensify when controlling for spatial spillovers, since the role of spatial context was already playing a relevant role from the beginning of the period analyzed. Therefore, although the ergodic distributions show a conditional-convergence pattern, addressing the problems of spatial exclusion fully, persistent polarization among geographical departments and populations, along with the relevant core-periphery gaps, still requires the design and implementation of specific policies.