Local Limit Research Articles

Extensive hypothesis testing for estimation of crash frequency models

Estimating crash data count models poses a significant challenge which requires extensive knowledge, experience, and meticulous hypothesis testing to capture underlying trends. Simultaneous consideration of multiple modelling aspects is required including, among others, functional forms, likely contributing factors, and unobserved heterogeneity. However, model development, frequently affected by time and knowledge, can easily overlook crucial modelling aspects such as identification of likely contributing factors, necessary transformations, and distributional assumptions. To facilitate model development and an estimation that can extract as many insights as possible, an optimization framework is proposed to generate and simultaneously test a diverse array of hypothesis. The framework comprises a mathematical programming formulation and three alternative solution algorithms. The objective function involves minimizing the Bayesian Information Criterion (BIC) to avoid overfitting. The solution algorithms include metaheuristics to deal with an NP-hard problem and search through a complex and nonconvex space. The metaheuristics also enable to handle unique datasets through varying search strategies. The effectiveness of the proposed framework was ascertained using three distinct datasets, and published models used as benchmarks. The results highlighted the ability of the proposed framework to estimate crash data count models, surpassing benchmark models in terms of insights and goodness-of-fit. The framework provides several advantages, such as robust hypothesis testing, uncovering unique specifications and vital insights in the data, and leveraging existing knowledge to enhance search efficiency. The framework also exposes the vulnerability of traditional analyst efforts to fall into local optima, bias, and limitations in creating more efficient models. In a compelling example using crash data from Washington, the proposed framework unveiled insights overlooked by a benchmark published model, identifying speed, interchanges, and grade breaks as likely crash contributors, and revealing the potential danger of excessively wide shoulders. Conversely, the benchmark model identified fewer contributing factors and missed a crucial non-linear relationship between crash safety and shoulder widths. While wider shoulders are typically associated with improved safety, the proposed models suggest a safety threshold beyond which further widening could decrease safety. The introduction of random parameters in the analysis revealed a more nuanced relationship with crash frequency, thereby underlining the limitations of models incapable of capturing heterogeneity.

Mechanistic mapping of random fields for stochastic finite element simulations of quasibrittle fracture

Spurious mesh sensitivity is a major challenge in continuum finite element (FE) simulations of damage and fracture of quasibrittle structures. It has been shown that the existing localization limiters, which largely focus on energy regularization, are insufficient for addressing the issue of mesh sensitivity in stochastic analysis. In this study, we investigate the mathematical algorithm for mapping the continuous random fields of material properties onto the FE meshes. This is a fundamental problem in stochastic FE analysis, which has profound implications for the mesh sensitivity in the prediction of the statistics of failure behavior. We adopt a continuum damage constitutive model, and develop a mechanistic mapping method. The projection of the random fields of material properties onto the FE mesh is governed by the prevailing damage pattern of the element. The damage pattern of each finite element is determined based on the spatial distribution of the damage of its surrounding elements. Meanwhile, the prevailing damage pattern also dictates the energy regularization of the constitutive response of the finite element. The combination of energy regularization and mechanistic mapping method ensures that, for each time increment, the random tangential stiffness tensor of each finite element is calculated in accordance with the ongoing damage pattern. A direct consequence of the model is that, depending on the damage pattern, the statistics of the tangential stiffness tensor could vary with the mesh size. The model is applied to stochastic FE analysis of both notched and unnotched flexural specimens under different loading configurations, which exhibit different failure behaviors. The numerical analysis also considers different correlation lengths of the random fields of material properties. The simulation shows that, with the energy regularization scheme, the commonly used local mapping and local averaging methods could yield considerable mesh dependence of the statistics of the peak load capacity. The result also reveals the effect of correlation length on the spurious mesh dependence. By relating the mapping algorithm to the underlying damage pattern, the present model is able to mitigate the mesh sensitivity for different specimen geometries, loading configurations, and correlation lengths.

Main drivers of dragonflies and damselflies (Insecta; Odonata) metacommunities in streams inside protected areas in the Brazilian Amazon.

The evaluation of environmental and spatial influence in freshwater systems is crucial for the conservation of aquatic diversity. So, we evaluated communities of Odonata in streams inside and outside sustainable use areas in the Brazilian western Amazon. We predicted that these streams would differ regarding habitat integrity and species α and β diversity. We also predict that environmental and spatial variables will be important for both suborders, but with more substantial effects on Zygoptera species, considering their nature of forest-specialist. The study was conducted in 35 streams, 19 inside and 16 outside sustainable use areas. The streams outside presented high species richness, abundance, and number of exclusive forest-specialist species from Zygoptera and higher scores of habitat integrity. In contrast, one sustainable use area presented the lowest values of these metrics. Besides, we found that environmental and spatial variables were significantly associated to Zygoptera species composition, but not with Anisoptera, which can be explained by their cosmopolitan nature. Our results indicated that an interplay between environmental and spatial processes determines the structure of the metacommunities of Zygoptera. The less effective dispersal rates and narrow ecological tolerance of Zygoptera species make them more influenced by local conditions and dispersal limitation, and more sensible to habitat modifications. We highlight the importance of improving the local management of the sustainable use areas by environmental agencies, mainly on areas that are losing their capacity to maintain the aquatic fauna, and implementation of social policies toward traditional people.

Induced Current Electro-Thermal Imaging for Breast Tumor Detection: A Numerical and Experimental Study.

This study proposes using magnetically induced currents in medical infrared imaging to increase the temperature contrast due to the electrical conductivity differences between tumors and healthy tissues. There are two objectives: (1) to investigate the feasibility of this active method for surface and deep tumors using numerical simulations, and (2) to demonstrate the use of this method through different experiments conducted with phantoms that mimic breast tissues. Tumorous breasts were numerically modeled and simulated in active and passive modes. At 750kHz, the applied current was limited for breast tissue-tumor conductivities (0.3S/m and0.75S/m) according to the local specific absorption rate limit of 10W/kg.Gelatin-based and mashed potato phantoms were produced to mimic tumorous breast tissues. In the simulation studies, the induced current changed the temperature contrast on the imaging surface, and the tumor detection sensitivity increased by 4mm.An 11-turn 70-mm-long solenoid coil was constructed, 20A current was applied for deep tumors, and a difference of up to 0.4 C was observed in the tumor location compared with the temperature in the absence of the tumor.Similarly, a 23-turn multi-layer coil was constructed, and a temperature difference of 0.4 C was observed. The temperature contrast on the body surface changed, and the tumor detection depth increased with the induced currents in breast IR imaging. The proposed active thermal imaging method was validated using numerical simulations and in vitro experiments.

On the Limits of Single Anchor Localization: Near-Field Versus Far-Field

On the Limits of Single Anchor Localization: Near-Field Versus Far-Field

Local weak limit of preferential attachment random trees with additive fitness

AbstractWe consider linear preferential attachment trees with additive fitness, where fitness is the random initial vertex attractiveness. We show that when the fitnesses are independent and identically distributed and have positive bounded support, the local weak limit can be constructed using a sequence of mixed Poisson point processes. We also provide a rate of convergence for the total variation distance between the r-neighbourhoods of a uniformly chosen vertex in the preferential attachment tree and the root vertex of the local weak limit. The proof uses a Pólya urn representation of the model, for which we give new estimates for the beta and product beta variables in its construction. As applications, we obtain limiting results and convergence rates for the degrees of the uniformly chosen vertex and its ancestors, where the latter are the vertices that are on the path between the uniformly chosen vertex and the initial vertex.

Some properties of combinatorial triangles related to Horadam polynomials

The Horadam polynomials unify many well-known polynomials, such as the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Jacobsthal polynomials and the Chebyshev polynomials. We investigate some properties of various combinatorial triangles related to Horadam polynomials, including their properties as almost-Riordan arrays and Riordan arrays, their total positivity, the real-rootedness of the generating functions of their rows, and the asymptotic normality (by central and local limit theorems).

3D Convolutional Neural Network-Based Multi-Parameter Video Quality Assessment Model on Cloud Platforms

In light of the rapid advancements in big data and artificial intelligence technologies, the trend of uploading local files to cloud servers to mitigate local storage limitations is growing. However, the surge of duplicate files, especially images and videos, results in significant network bandwidth wastage and complicates server management. To tackle these issues, we have developed a multi-parameter video quality assessment model utilizing a 3D convolutional neural network within a video deduplication framework. Our method, inspired by the analytic hierarchy process, thoroughly evaluates the effects of packet loss rate, codec, frame rate, bit rate, and resolution on video quality. The model employs a two-stream 3D convolutional neural network to integrate spatial and temporal streams for capturing video distortion details, with a coding layer configured to remove redundant distortion information. We validated our approach using the LIVE and CSIQ datasets, comparing its performance against the V-BLIINDS and VIDEO schemes across different packet loss rates. Furthermore, we simulated the client-server interaction using a subset of the dataset and assessed the scheme's time efficiency. Our results indicate that the proposed scheme offers a highly efficient solution for video quality assessment.

A local central limit theorem for random walks on expander graphs

A local central limit theorem for random walks on expander graphs

Local central limit theorem for real eigenvalue fluctuations of elliptic GinOE matrices

Local central limit theorem for real eigenvalue fluctuations of elliptic GinOE matrices

Local limits of random bipartite maps in high genus: the general case

Local limits of random bipartite maps in high genus: the general case

Classical and almost sure local limit theorems

Classical and almost sure local limit theorems

Локальная предельная теорема для ветвящихся случайных систем Гальтона–Ватсона с иммиграцией и бесконечной дисперсией

The paper considers a stochastic population growth model, which is the critical Galton-Watson stochastic branching system allowing immigration. We consider the case when the mathematical expectation of the law of influx of immigrant particles and the variance of the law of reproduction of aboriginal particles have infinite values. The asymptotic properties of transition probabilities are studied in the case when the states of the system are irreversible. For this case, a local limit theorem has been established.

FAST FOURIER TRANSFORM METHOD FOR PERIDYNAMIC BAR OF PERIODIC STRUCTURE

The basic feature of the peridynamics [introduced by Silling (2000)] considered is a continuum description of material behavior as the integrated nonlocal force interactions between infinitesimal material points. A heterogeneous bar of the periodic structure of constituents with peridynamic mechanical properties is analyzed. One introduces the volumetric periodic boundary conditions (PBCs) at the interaction boundary of a representative unit cell (UC), whose local limit implies the known locally elastic PBCs. This permits us to generalize the classical computational homogenization approach to its counterpart in peridynamic micromechanics (PM). Alternative to the finite element methods (FEM) for solving computational homogenization problems are the fast Fourier transforms (FFTs) methods developed in local micromechanics (LM). The Lippmann-Schwinger (L-S) equation-based approach of the FFT method in the LM is generalized to the PM counterpart. Instead of one convolution kernel in the L-S equation, we use three convolution kernels corresponding to the properties of the matrix, inclusions, and interaction interface. The Eshelby tensor in LM depending on the inclusion shape is replaced by PM counterparts depending on the inclusion size and interaction interface (although the Eshelby concept of homogeneous eigenfields does no work in PM). The mentioned tensors are estimated one time (as in LM) in a frequency domain (also by the FFT method). Numerical examples for 1-D peridynamic inhomogeneous bar are considered. Computational complexities O (N <i>log</i><sub>2</sub> N) of the FFT methods are the same in both LM and PM.

Exotic local limit theorems at the phase transition in free products

Exotic local limit theorems at the phase transition in free products

A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three

A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three

Effects of physician therapy sessions on depression – Evidence-based practices

This research study investigates the impact of physician therapy sessions on individuals suffering from depression. It examines the effectiveness of therapy as an evidence-based practice in the management of depression. Three distinct research papers were reviewed to investigate the effects of therapy sessions on physician burnout. Each study employed various methodologies, including surveys, interventions and qualitative analyses. Gender differences were also examined as a potential variable. Paper one concluded that despite being valuable support mechanisms, debriefing sessions did not significantly reduce burnout syndrome. In contrast, Paper Two and Paper Three reported a significant decrease in burnout following the interventions. All three papers found that gender was the only variable that changed. While the scores of the Maslach Burnout Inventory did not change in Paper One, the debriefing sessions were appreciated and accepted by the participants. Paper Three provided in-depth information, including examples, to enhance comprehension. Two out of the three papers concluded that implementing therapy sessions, such as counselling, cognitive-behavioural therapy, mindfulness-based stress reduction, group therapy, and mindfulness workshops, for physicians can prevent burnout syndrome. The third paper showed no significant change, suggesting that exclusive therapy sessions may need to be combined with other solutions, such as mindfulness practices or reduced working hours. These findings have the potential to inform practice changes, including updated clinical guidelines, new term protocols, enhanced screening and prevention strategies, quality improvement initiatives, training and education feedback, adaptation, monitoring, and evaluation. Overcoming barriers such as knowledge, skills, resources, motivation, attitude, and organisational culture is crucial for the successful implementation of evidence-based practices (EBP). Further, international research is needed to identify local limitations and advantages. This topic offers valuable insights into EBP and its role in improving patient outcomes, with the ultimate goal of reducing physician burnout and enhancing the quality of patient care.

Multiscale simulation of highly heterogeneous subsurface flow with physically adaptive 3D unstructured grids

The multiscale finite volume framework is extended with physical-based grid adaptation (MSFV-GA) for three-dimensional fully unstructured grids. The MSFV method produces large errors for highly heterogeneous and anisotropic problems on standard coarse grids generated based on geometrical features. Adding constraints based on the fine-scale physical properties to construct coarse grids can increase the accuracy and robustness of the MSFV solutions. A novel and automated coarse grid generation strategy adaptable to the reservoir heterogeneity for 3D unstructured grids is presented. Adaptive coarse grids are generated based on local variations of fine scale permeability field. The proposed procedure is very flexible respect to the local physical and geometrical limitations in coarse blocks. Multiscale coarse grid adaptation notably improves the basis functions calculations. The performance of the MSFV-GA in handling challenging problems involving high media contrasts or impermeable shale layers is assessed. The results are very promising and show that the MSFV-GA can accurately approximate complex physics problems. The presented 3D unstructured procedure can notably improve the applicability of the multiscale finite volume method and provide a promising framework for the next generation of reservoir flow simulators.

ET-PDA: An event-triggered parameter distributed accelerated algorithm for economic dispatch problems

In this paper, we consider a distributed economic dispatch problem (EDP) in smart grids, where each generator only communicates with its neighbors and minimizes its own cost in the presence of network-wide equality constraints and local capacity limits. Distributed algorithms to solve this problem have become an attractive focus of engineering research due to their multiple advantages. Many existing methods are time-triggered, whereas few works have been dedicated to solving the problem using an event-triggered approach. This problem gets more challenging when further accelerated convergence is desired. To solve such a problem, we carefully design an event-triggered parameter distributed accelerated algorithm, named as ET-PDA. On the one hand, the choice of different parameters in ET-PDA will lead to different momentum (Nesterov or heavy-ball) methods, which facilitates the accelerated convergence of the algorithm. On the other hand, the event-triggered mechanism in ET-PDA makes the time gap between two continuous interaction moments of each generator larger than the iteration interval, contributing to improved communication efficiency. In particular, ET-PDA achieves linear convergence when the local cost function of each generator is smooth and strongly convex, moreover, it precludes Zeno-like behavior. The effectiveness of ET-PDA is also verified through a series of simulation experiments.

The Mechanism of Titanium Hydride Formation on Grade-2 Titanium

ASTM Grade-2 titanium (Ti-2) is a commercially pure grade widely used for its corrosion resistance in extreme environments. Therefore, Ti-2 has found applications within industries such as oil and gas, chemical processing, and nuclear power, where it is used for components such as reaction vessels, piping, and heat exchangers. Challenges with the fabrication process result in relatively high amounts of iron in commercial materials such as Grade-2, Grade-7, and Grade-12, which all have a maximum tolerance of 0.3 wt.% iron.The amount of iron present in titanium has been shown to have a significant effect on the microstructure and corrosion behaviour[1]. For example, Fe will precipitate and form TixFe intermetallic particles (IMPs) along grain boundaries if the local solubility limit is exceeded. Many of the corrosion processes (e.g., crevice corrosion) that determine the long-term integrity of Ti are strongly affected by the presence of IMPs[1]. Another detrimental corrosion scenario is the formation of titanium hydride (TiHx), which can precipitate on the surface and/or in the bulk material when the hydrogen concentration is high enough. Formation of TiHx phases increases the susceptibility of the metal to cracking, as the hydride is less ductile than the metal and its formation results in a strain-inducing volume increase within the matrix. Despite the proven importance of IMPs to the corrosion behaviour of Ti, and the detrimental effects of hydride formation on the material’s integrity, a direct relationship between IMPs and TiHx formation is not well established. There is some evidence that titanium hydride formation initiates at IMPs[2], but a complete mechanistic understanding is missing.In this study, the initiation and propagation mechanism of TiHx formation on Ti-2 is being investigated over a 24-hour period. Hydrides were grown galvanostatically in a simulated crevice corrosion environment. The surface was analyzed at various times using field emission scanning electron microscopy (FE-SEM), energy-dispersive X-ray spectroscopy (EDX), focused ion beam (FIB) milling, and X-ray diffraction (XRD). By visualizing TiHx within the matrix using FE-SEM, we determined that titanium hydride formation initiates at IMPs and then grows both laterally and vertically around the IMP. After reaching a depth of ~ 4 µm below the surface of the IMP, the hydride stops growing vertically but continues to spread laterally across the Ti grain face until full surface coverage is reached. Finally, a steady-state condition is reached, in which hydride is present as a uniformly distributed layer across the surface with a thickness of ~ 4 μm. Additionally, the electrochemical potential values during the galvanostatic hydride growth process and the amount of hydride detected using XRD both support the hypothesis of the hydride growing rapidly before reaching a limited thickness.[1] X. He, J. J. Noël, D. W. Shoesmith, Corrosion 2004, 60, 378–386.[2] Q. Tan, Z. Yan, H. Wang, D. Dye, S. Antonov, B. Gault, Scr. Mater. 2022, 213, 114640.