Period Map Research Articles

CNOSSOS-FR: Are current road traffic noise emission coefficients still representative of today's vehicle fleet and roads?

CNOSSOS-EU is the common noise prediction method for producing strategic noise maps in Europe, according to Directive 2002/49/CE. Its road vehicle noise emission model involves a propulsion noise component and a rolling noise component, with coefficients specific to each vehicle category. As currently applied in France, it relies on the original EU coefficients published in the 2015 CNOSSOS-EU version and the rolling noise contribution is detailed in road surface classes in agreement with the national NMPB2008 method. As provided in the European method, corrective coefficients in frequency bands were determined per road surface class. The objective was to minimise the overall difference between NMPB2008 and CNOSSOS-FR emission predictions under similar conditions, the former method being previously used for periodic mapping. Now considering the later release of new EU reference coefficients and the difficulty of making the two methods involving different expressions and assumptions coincide, as well as questioning the need to update emission values resulting from measurements of the vehicle fleet taken 20-25 years ago, the study MINOOS is being carried out to assess the noise emission of the current vehicle fleet and reconsider French prediction coefficients accordingly. The paper describes the procedure and presents the first results.

Deformations and rigidity for mixed period maps

Deformations and rigidity for mixed period maps

Estimation of soil organic matter content by combining Zhuhai-1 hyperspectral and Sentinel-2A multispectral images

Hyperspectral satellite imagery has significant advantages in rapidly monitoring soil organic matter (SOM) content over a large area. However, limitations in the timely acquisition of site-specific data may affect its effectiveness due to weather influences and revisit cycles. This paper proposes a novel method for estimating SOM content that combines the high temporal resolution of the Zhuhai-1 hyperspectral satellite image and Sentinel-2A multispectral satellite image to broaden the spectral range of Zhuhai-1 images. Multisource features, including spectral bands, topographic features, textural features, and spectral indexes, are extracted from the combined image and digital elevation model. An improved genetic algorithm (IGA) is proposed to optimize feature selection and extreme gradient boosting (XGBoost) is then applied to estimate SOM content. The proposed method was validated using 197 topsoil samples and satellite images collected from a demonstration area in Lishu County, Jilin Province, China. The results indicate that the estimation accuracy using the combined image was greater than using one single image. Compared with only using the Sentinel-2A and Zhuhai-1 images, the coefficient of determination (R2) values improved from 0.61 and 0.73 to 0.82, the ratio of the prediction to the deviation (RPD) values improved from 1.62 and 1.93 to 2.35, and the ratio of performance to the interquartile distance (RPIQ) values improved from 2.16 and 2.58 to 3.15, respectively. Furthermore, the XGBoost algorithm outperformed the random forest algorithm in terms of model accuracy and mapping reliability. The use of multisource features improved the R2 value from 0.45 to 0.82 compared to only using 31 spectral bands of Zhuhai-1 and Sentinel-2A image, with contribution rates in descending order of spectral indexes (48.2%), topographic features (24.7%), spectral bands (19.9%), and textural features (7.2%). This paper thus presents a promising method for efficient periodic mapping of the SOM content by combining data from a hyperspectral satellite constellation and a multispectral satellite image.

Interpretation of Microtremor Data Through Analysis Horizontal to Vertical Spectral Ratio (HVSR) for Microzonation of Seismic Earthquake Hazards in Baubau City

Research has been carried out on seismic hazard microzonation in the city of Bau – bau using microtremor data. The aim of this research is to determine the seismic vulnerability index based on horizontal to vertical spectral ratio (HVSR) analysis and create a dominant frequency microzonation map (F0), dominant period map (T0), amplification factor map (A0), and seismic vulnerability index map (Kg) from microtremor data which can describe the level of vulnerability of an area to seismic hazards. Microtremor measurements were carried out using a portable three-component seismograph (TDS. 303), the data was analyzed with gepsy software via the HVSR method. The research results show that the distribution of dominant frequency values ​​(F0), ranges from 0.4795 Hz to 16.6383 Hz, dominant period values ​​(T0), ranges from 0.0601 seconds to 2.0854 seconds, amplification factor values ​​(A0), ranges from 1.2285 to 4.9043, and the seismic vulnerability index (Kg) value ranges from 0.1043 to 11.0276. The values ​​(F0), (T0), (A0), and (Kg) are interpreted by referring to literature data and surface geological maps of the research area. The results show that the study area has a small portion of sediment layers that are vulnerable to seismic hazards.

Projective structures and Hodge theory

AbstractEvery compact Riemann surface X admits a natural projective structure $$p_u$$ p u as a consequence of the uniformization theorem. In this work we describe the construction of another natural projective structure on X, namely the Hodge projective structure $$p_h$$ p h , related to the second fundamental form of the period map. We then describe how projective structures correspond to (1, 1)-differential forms on the moduli space of projective curves and, from this correspondence, we deduce that $$p_u$$ p u and $$p_h$$ p h are not the same structure.

Weak localization in radiative transfer of acoustic waves in a randomly-fluctuating slab

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of local effects, both on the (small) scale of the wavelength, are observed: one within one wavelength of the boundaries of the slab, and one inside the domain (at a distance from the boundaries large compared to the wavelength). The former impacts the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

Infinite metacyclic subgroups of the mapping class group

For g\geq 2 , let \mathrm{Mod}(S_{g}) be the mapping class group of the closed orientable surface S_{g} of genus g . In this paper, we provide necessary and sufficient conditions for a pair of elements in \mathrm{Mod}(S_{g}) to generate an infinite metacyclic subgroup. In particular, we provide necessary and sufficient conditions under which a pseudo-Anosov mapping class generates an infinite metacyclic subgroup of \mathrm{Mod}(S_{g}) with a nontrivial periodic mapping class. As applications of our main results, we establish the existence of infinite metacyclic subgroups of \mathrm{Mod}(S_{g}) isomorphic to \mathbb{Z}\rtimes\mathbb{Z}_{m} , \mathbb{Z}_{n}\rtimes\mathbb{Z} , and \mathbb{Z}\rtimes\mathbb{Z} . Furthermore, we derive bounds on the order of a nontrivial periodic generator of an infinite metacyclic subgroup of \mathrm{Mod}(S_{g}) that are realized. Finally, we show that the centralizer of an irreducible periodic mapping class F is either \langle F\rangle or \langle F\rangle\times\langle i\rangle , where i is a hyperelliptic involution.

Monitoring of Plant Ecological Units Cover Dynamics in a Semiarid Landscape from Past to Future Using Multi-Layer Perceptron and Markov Chain Model

Anthropogenic activities and natural disturbances cause changes in natural ecosystems, leading to altered Plant Ecological Units (PEUs). Despite a long history of land use and land cover change detection, the creation of change detection maps of PEUs remains problematic, especially in arid and semiarid landscape. This study aimed to determine and describe the changes in PEUs patterns in the past and present, and also predict and monitor future PEUs dynamics using the multi-layer perceptron-Markov chain (MLP-MC) model in a semiarid landscape in Central Zagros, Iran. Analysis of PEUs classification maps formed the basis for the identification of the main drivers in PEUs changes. First, an optimal time-series dataset of Landsat images were selected to derive PEUs classification maps in three periods, each separated by 16 years. Then, PEUs multi-temporal maps classified for period 1 (years 1986–1988) period 2 (years 2002–2004), and period 3 (years 2018–2020) were employed to analyze and predict PEUs dynamics. The dominant transitions were identified, and the transition potential was determined by developing twelve sub-models in the final change prediction process. Transitions were modeled using a Multi-Layer Perceptron (MLP) algorithm. To predict the PEU map for period 3, two PEUs classification maps of period 1 and period 2 were used using the MLP-MC method. The classified map and the predicted map of period 3 were used to evaluate and validate the predicted results. Finally, based on the results, transitions of future PEUs were predicted for the year 2036. The MLP-MC model proved to be a powerful model that can predict future PEUs dynamics that are the result of current human and managerial activities. The findings of this study demonstrate that the impact of anthropogenic processes and management activities will become visible in the natural environment and ecosystem in less than a decade.

An Example of Turkish-Tatar Urbanism in Siberia: Kyzyl Tura

This study examines the geographical location, historical origins, and socio-economic and political dynamics of Kyzyl (Kızıl) Tura, a city situated in Siberia and inhabited by the Turkish-Tatar population. Emir Timur's military expeditions in the second half of the 14th century led to a decline in trade along the Trans-Asian road system and subsequently caused international trade to move to Trans-Siberia. In Siberia, the construction of new Turkish-Tatar cities and the expansion of already existing settlements started at the same time. The main argument of this study is that the presence of the Turkish-Tatar population in Siberia was considerable. Additionally, it suggests that the Turkish-Tatar urbanisation and commercial network played a significant role in the historical development of the region, as exemplified by the case of Kyzyl Tura. The objective of this study is to provide advantages to researchers in the field by demonstrating that the Turkish-Tatar presence in the region, as well as the subsequent changes in demographic and political structures following Russian colonisation, have exhibited variations throughout history. The study engaged in a comparative evaluation of data obtained from primary sources and contemporary literature. The utilisation of Russian chronicles and period maps was done. This study seeks to gather comprehensive information on Kyzyl Tura and provide evidence of Turkish-Tatar urbanism in Siberia through the examination of Kyzyl Tura. Research has demonstrated a deterioration in the transport network and trade after the settlement of Russians in numerous Turkish-Tatar cities in Siberia.

Spectral stability of periodic traveling wave solutions for a double dispersion equation

ABSTRACT In this article, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method, we find explict periodic waves and we also present a characterization for all positive and periodic solutions for the model using the monotonicity of the period map in terms of the energy levels. The monotonicity of the period map is also useful to obtain the quantity and multiplicity of non-positive eigenvalues for the associated linearized operator and to do so, we use tools of the Floquet theory. Finally, we prove the spectral stability by analyzing the difference between the number of negative eigenvalues of a convenient linear operator restricted to the space constituted by zero-mean periodic functions and the number of negative eigenvalues of the matrix formed by the tangent space associated to the low order conserved quantities of the evolution model.

Applications of the Clifford torus to material textures

This paper introduces a new 2D representation of the orientation distribution function for an arbitrary material texture. The approach is based on the isometric square torus mapping of the Clifford torus, which allows for points on the unit quaternion hypersphere (each corresponding to a 3D orientation) to be represented in a periodic 2D square map. The combination of three such orthogonal mappings into a single RGB (red–green–blue) image provides a compact periodic representation of any set of orientations. Square torus representations of five different orientation sampling methods are compared and analyzed in terms of the Riesz s energies that quantify the uniformity of the samplings. The effect of crystallographic symmetry on the square torus map is analyzed in terms of the Rodrigues fundamental zones for the rotational symmetry groups. The paper concludes with example representations of important texture components in cubic and hexagonal materials. The new RGB representation provides a convenient and compact way of generating training data for the automated analysis of material textures by means of neural networks.

Accuracy Evaluation for Plan-Reliefs and Historical Maps Created during WWI in Northern Italy

The availability of digital copies of historical artifacts modeling the territory through the so-called “plan-reliefs” is important for many reasons: the preservation of the artifact if the physical object is damaged or destroyed, the possibility of creating virtual showrooms and providing researchers a tool to study the object combining information from different sources. For these reasons, a set of plan-reliefs created during World War I on the Italian front and kept by the Italian Historical War Museum of Rovereto (Italy) was surveyed to create digital models of the surfaces, which were georeferenced in the ETRS89 datum. A set of historical military maps of the same period was georeferenced to overlay the sets to the surface in the digital representation and to try to infer clues about the cartographic sources used in the historical artifact creation. The best transformation for georeferencing the maps is different depending on the map scale, map origin, conservation status and number of Ground Control Points. The georeferencing process precision and accuracy were evaluated. The digital models created in this study were compared to the official Digital Terrain Model (DTM) provided by the Regions or the autonomous provinces. The results demonstrate the feasibility of the approach, and the combination of the models with the georeferenced maps is used by historians to describe the process used in the creation of plan-reliefs.

Analysis of the period map for a singular ODE related to the Liebau phenomenon

We study the positive periodic solutions of a periodically perturbed second-order nonlinear equation with a singularity, related to the so-called Liebau phenomenon, which has received great deal of interest in the past decade. Our main contribution concerns a global theorem about the monotonicity of the period map for the equation with constant coefficients. Then, as applications, we prove new bifurcation results for periodic solutions (harmonic and subharmonic), as well as the presence of complex dynamics for some periodic coefficients which are meaningful from a physical point of view.

InVAErt networks: A data-driven framework for model synthesis and identifiability analysis

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system analysis including model inversion and identifiability. We introduce InVAErt (pronounced invert) networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally analyze how changes in the penalty coefficients affect the stationarity condition of the loss function, the phenomenon of posterior collapse, and propose strategies for latent space sampling, since we find that all these aspects significantly affect both training and testing performance. We verify our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.

Categorical Torelli theorems for Gushel–Mukai threefolds

AbstractWe show that a general ordinary Gushel–Mukai (GM) threefold can be reconstructed from its Kuznetsov component together with an extra piece of data coming from tautological subbundle of the Grassmannian . We also prove that determines the birational isomorphism class of , while determines the isomorphism class of a special GM threefold if it is general. As an application, we prove a conjecture of Kuznetsov–Perry in dimension 3 under a mild assumption. Finally, we use to restate a conjecture of Debarre–Iliev–Manivel regarding fibers of the period map for ordinary GM threefolds.

Multiple-point geostatistics-based spatial downscaling of heavy rainfall fields

High-resolution gridded rainfall products at sub-daily and 100 km scales are required for hydrological applications in mountainous and urban catchments. As most catchments are ungauged, gridded rainfall data are often obtained through remote sensing. However, their spatial resolution is often too coarse (at 101 km) and requires to be downscaled to a finer resolution. The challenge is not only to downscale the rainfall intensity to a finer scale by considering areal reduction factors, but also the spatial structure of the storm, as both elements are equally important to the assessment of the surface hydrological response. As a result of the lack of training data, the latter is difficult to obtain. Further development of the stochastic multiple-point geostatistics (MPS) framework is presented to downscale long-term satellite-derived gridded rainfall series using only a few years of high-resolution rainfall observations. We demonstrate how the MPS framework can be used to downscale the satellite-derived CMORPH rainfall from 8 to 1 km resolution for 1998–2019, taking the city of Beijing as a case study, with a specific focus on extreme rainfall events. The high-resolution multisource-merged CMPAS dataset (1 km, hourly), available for 2015–2020, is used as the source of the training images. We show that the downscaling framework preserves the observed mean areal rainfall (with a bias of 2 %), reproduces the spatial coefficient of variance (with a similar bias), and also retains extreme rainfall at the 99th percentile (with a bias of 6 %). Furthermore, it adequately reproduces the rainfall spatial structure, preserving the variograms of the rainfall fields. Similarities were also observed comparing the 2- to 30-year return period maps of the downscaled rainfall extreme with ground observations, with half of the stations (10 out of 19) agreeing on the location and intensity of the extreme rainfall for all return periods. The results indicate that our framework downscales rainfall intensities and preserves the spatial structure well, especially for heavy rainfall, even if limited data is available. The proposed approach can be applied to other rainfall datasets and regions.

Transformer Fault Diagnosis Method Based on SCA-VMD and Improved GoogLeNet

Aiming at the influence of the fundamental frequency and its harmonics in transformer vibration signals on fault signals, which cause a low fault identification rate and degradation of classification model performance, a new strategy is proposed for fault diagnosis using periodic map spectrum feature maps as input features. In this study, the optimal decomposition parameters were first found adaptively using the VMD improved by the positive cosine optimisation algorithm; then, the transformer vibration signal was modally decomposed, and the periodic map spectrum features were plotted according to the differences in the energy distribution of the different modal components at different frequencies. Finally, the GoogLeNet classification model with the improved attention mechanism assigned different weights to the feature maps in both spatial and channel dimensions to improve the classification accuracy and achieve transformer fault diagnosis. The experimental results verified the validity of the adopted feature map and the proposed model, and the accuracy was significantly improved to 99.04% compared with the traditional GoogLeNet, which is valuable for engineering applications.

Shallow three-dimensional shear wave velocity model for the Mexico City Basin

In this study, a simplified shallow three-dimensional shear wave velocity (Vs) model is presented for the Mexico City Basin. To this end, previous studies were carefully reviewed to assemble a database of Vs and site period measurements for the region. The new site period measurements obtained at the western edge of the Basin were compared to the existing 2004 Complementary Technical Standards of Mexico site period nominal map, (NTC, 2004) the Lermo et al. (2020) site period map, and Design Seismic Actions System (SASID), 2020 site period predictions. Each site period prediction method was shown to have differences with respect to the new measurements along the western edge of the Basin. However, there was no bias for the prediction methods with the Lermo et al. (2020) and SASID predictions, demonstrating less error between the measured values than the NTC (2004) predictions. To develop the three-dimensional Vs model, the shallow (top 60 m) subsurface was divided into five generalized soil layers. The site period was used as the only input for the three-dimensional Vs model to simplify and maximize the model’s applicability. The performance of the model was assessed by comparing the measured and predicted Vs profiles. Overall, the three-dimensional Vs model developed in this study is a valuable tool that can be used along with geophysical estimates of deeper structure for ground motion modeling and preliminary site response studies along with other benefits to the seismic resiliency of the region.

Emergent scalar symmetry in discrete dynamical systems

Discrete quadratic dynamical systems are frequently used to define models of reality. To understand these recursive systems is to know the behavior of their complex orbits. The Mandelbrot Set plays an important role in this: the behavior of the orbits of its points can be extrapolated to all quadratic polynomials. In calculating the map of periods for the orbits of the points belonging to the Mandelbrot Set by means of discrete (and finite) encoding, some singular points called symmetrical points appear on the map. Such points configure, in a surprisingly harmonic and regular manner, the values of the rest of points in the map of periods. Thus, knowing these points and their properties is extremely helpful to better understand the behavior of quadratic and discrete dynamical systems. Important properties of such points are described in this article. We emphasize the emergent scalar symmetry property, which appears as a consequence of the finiteness of discrete values with which we are inevitably limited to represent the continuum. Thanks to this property, the images created around these points are not altered when removing or selecting one of their several pixel rows and columns. The image can be sampled in its vicinity, at any scale, without losing information regarding the vicinity. We propose a justification on why the map of periods is highly hypersensitive to small changes in the parameters defining the calculation mode of the map.

A Multivariate Frequency Analysis Framework to Estimate the Return Period of Hurricane Events Using Event‐Based Copula

AbstractThis study proposed a framework to evaluate multivariate return periods of hurricanes using event‐based frequency analysis techniques. The applicability of the proposed framework was demonstrated using point‐based and spatial analyses on a recent catastrophic event, Hurricane Ian. Univariate, bivariate, and trivariate frequency analyses were performed by applying generalized extreme value distribution and copula on annual maximum series of flood volume, peak discharge, total rainfall depth, maximum wind speed, wave height and storm surge. As a result of point‐based analyses, return periods of Hurricane Ian was investigated by using our framework; univariate return periods were estimated from 39.2 to 60.2 years, bivariate from 824.1 to 1,592.6 years, and trivariate from 332.1 to 1,722.9 years for the Daytona‐St. Augustine Basin. In the Florida Bay‐Florida Keys Basin, univariate return periods were calculated from 7.5 to 32.9 years, bivariate from 36.5 to 114.9 years, and trivariate from 25.0 to 214.8 years. Using the spatial analyses, we were able to generate the return period map of Hurricane Ian across Florida. Based on bivariate frequency analyses, 18% of hydrologic unit code 8 (HUC8) basins had an average return period of more than 30 years. Sources of uncertainty, due to the scarcity of analysis data, stationarity assumption and impact of other weather systems such as strong frontal passages, were also discussed. Despite these limitations, our framework and results will be valuable in disaster response and recovery.