Period Map Research Articles

Shear wave velocity and site period measurements for the western portion of the Mexico City Basin following the Mw7.1 2017 Puebla–Morelos, Mexico, earthquake

Dynamic site characterization was performed at 25 sites located on the western portion of the Mexico City Basin that were severely damaged during the Mw7.1 2017 Puebla–Morelos, Mexico, earthquake. Testing was conducted using active and passive seismic surface wave methods and the microtremor horizontal-to-vertical spectral ratio method to determine site periods and develop one-dimensional (1D) shear wave velocity ( Vs) profiles for the first 60 m of the subsoil. The measured site periods were compared to site period maps developed in 2004 and 2020 along with values computed using the Design Seismic Actions System (SASID) software following the 2020 version of the Complementary Technical Norms for Seismic Design (NTC-DS). The most noticeable biases in the predictions from the 2004 site period map were observed between the boundary of Zone II and Zone IIIa, at which site periods are overestimated. These estimates were improved upon in the 2020 site period map and showed a close similarity with SASID computed site period values. The Vs, depth, and thickness of the lacustrine clay layer were also determined to be quite variable within the basin. The softest sites are located between the lakebeds with a Vs between 45 and 57 m/s. Sites located toward the outer rim of the North lakebed have a higher Vs between 80 and 100 m/s. The thickness of the clay layer varies significantly in the western side of the Basin with values ranging between approximately 3 and 34 m. Overall, the results of this study indicate good agreement with the model embedded in the SASID software. The results (1) emphasize the need to regularly monitor changes that occur over time in the lacustrine clay layer, (2) complement the development of models that improve our understanding of wave propagation within the Basin, and (3) update and improve Mexico City’s Norms.

Extreme temperature trend and return period mapping in a changing climate in Upper Tekeze river basin, Northern Ethiopia

There is a consensus that global warming leads to the frequent occurrence of extreme temperature events that significantly impact human life, water resources, agricultural production, and ecosystems. However, the magnitudes of projected temperatures and the probabilities of extreme event occurrences are still deficient for robust planning and early warning efforts at major river basins. This study aimed to analyze extreme temperature trends and mapping return periods in a changing climate for the case of the upper Tekeze river basin, Northern Ethiopia. The future temperature is projected based on global climate models (GCMs) under RCP 4.5 and RCP 8.5 scenarios. The annual extreme temperatures were obtained from the daily temperature data series for the 12 stations by applying the block maxima series method. The non-parametric Mann-Kendall (M-K) statistical test was used for trend detection. The inverse distance weighted (IDW) method has been used to interpolate the point data and reveal the spatial patterns of the extreme temperature of the 50-year return period. The result shows the future extreme temperature will rise by 0.6–2.2 °C. Moreover, the future extreme temperature revealed a significant increasing trend in most of the stations (around 66.3%). The spatial extent of the 50-year return period of the extreme temperature map showed that in the future (2022–2051), the extreme temperature will be increased by 0.2–3.4 °C compared to the baseline period (1980–2009). The extreme temperature trend and return period mapping under climate change will help better local plans and fine-tune mitigation and adaptation measures.

A note on augmented period maps

A note on augmented period maps

Redes empresariales y administración estatal: La provisión de materiales estratégicos en el mundo hispánico durante el largo siglo XVIII

Redes empresariales y administración estatal: La provisión de materiales estratégicos en el mundo hispánico durante el largo siglo XVIII

Conceptual and Analytical Framework as Flood Risk Mapping Subsidy

There are still gaps in defining values and category classifications of exposed items in quantitative damage analysis. This paper proposes a framework that refines the development of flood risk analysis at a local scale. This study first performs a quantitative risk analysis, based mainly on secondary data; it then attempts to communicate the results graphically, aiming to reduce the financial and human resources required. We propose an easily standardized database in a GIS environment, analyzing the influence of a reservoir for flood control and the construction of replicable local-scale risk curves. Hydrological (HEC-HMS) and 2D hydrodynamic (HEC-RAS) models were used to simulate hydrographs considering different return periods. For damage estimation, the processing included vectorization of lots, building use definition with Google Street View, classification of standard designs, and a field survey to validate those classes. In monetary value, this study calculated the effect of the construction of a reservoir for damage reduction, showing the potential to determine the effectiveness of measures adopted to mitigate flood impacts. In addition, for each simulated return period, exposure, hazard, and damage maps can be established, making it possible to perform a complete risk analysis.

Towards high-accuracy classifying attention-deficit/hyperactivity disorders using CNN-LSTM model

Objective. The neurocognitive attention functions involve the cooperation of multiple brain regions, and the defects in the cooperation will lead to attention-deficit/hyperactivity disorder (ADHD), which is one of the most common neuropsychiatric disorders for children. The current ADHD diagnosis is mainly based on a subjective evaluation that is easily biased by the experience of the clinicians and lacks the support of objective indicators. The purpose of this study is to propose a method that can effectively identify children with ADHD. Approach. In this study, we proposed a CNN-LSTM model to solve the three-class problems of classifying ADHD, attention deficit disorder (ADD) and healthy children, based on a public electroencephalogram (EEG) dataset that includes event-related potential (ERP) EEG signals of 144 children. The convolution visualization and saliency map methods were used to observe the features automatically extracted by the proposed model, which could intuitively explain how the model distinguished different groups. Main results. The results showed that our CNN-LSTM model could achieve an accuracy as high as 98.23% in a five-fold cross-validation method, which was significantly better than the current state-of-the-art CNN models. The features extracted by the proposed model were mainly located in the frontal and central areas, with significant differences in the time period mappings among the three different groups. The P300 and contingent negative variation (CNV) in the frontal lobe had the largest decrease in the healthy control (HC) group, and the ADD group had the smallest decrease. In the central area, only the HC group had a significant negative oscillation of CNV waves. Significance. The results of this study suggest that the CNN-LSTM model can effectively identify children with ADHD and its subtypes. The visualized features automatically extracted by this model could better explain the differences in the ERP response among different groups, which is more convincing than previous studies, and it could be used as more reliable neural biomarkers to help with more accurate diagnosis in the clinics.

On perturbations of algebraic periodic automorphisms of a two-dimensional torus

According to the results of V. Z. Grines and A. N. Bezdenezhnykh, for each gradient-like diffeomorphism of a closed orientable surface M2 there exist a gradient-like flow and a periodic diffeomorphism of this surface such that the original diffeomorphism is a superposition of a diffeomorphism that is a shift per unit time of the flow and the periodic diffeomorphism. In the case when M2 is a two-dimensional torus, there is a topological classification of periodic maps. Moreover, it is known that there is only a finite number of topological conjugacy classes of periodic diffeomorphisms that are not homotopic to identity one. Each such class contains a representative that is a periodic algebraic automorphism of a two-dimensional torus. Periodic automorphisms of a two-dimensional torus are not structurally stable maps, and, in general, it is impossible to predict the dynamics of their arbitrarily small perturbations. However, in the case when a periodic diffeomorphism is algebraic, we constructed a one-parameter family of maps consisting of the initial periodic algebraic automorphism at zero parameter value and gradient-like diffeomorphisms of a twodimensional torus for all non-zero parameter values. Each diffeomorphism of the constructed one-parameter families inherits, in a certain sense, the dynamics of a periodic algebraic automorphism being perturbed.

A Global Analysis of the Spatial and Temporal Variability of Usable Landsat Observations at the Pixel Scale

The Landsat program has the longest collection of moderate-resolution satellite imagery, and the data are free to everyone. With the improvements of standardized image products, the flexibility of cloud computing platforms, and the development of time series approaches, it is now possible to conduct global-scale analyses of time series using Landsat data over multiple decades. Efforts in this regard are limited by the density of usable observations. The availability of usable Landsat Tier 1 observations at the scale of individual pixels from the perspective of time series analysis for land change monitoring is remarkably variable both in space (globally) and time (1985–2020), depending most immediately on which sensors were in operation, the technical capabilities of the mission, and the acquisition strategies and objectives of the satellite operators (e.g., USGS, commercial company) and the international ground receiving stations. Additionally, analysis of data density at the pixel scale allows for the integration of quality control data on clouds, cloud shadows, and snow as well as other properties returned from the atmospheric correction process. Maps for different time periods show the effect of excluding observations based on the presence of clouds, cloud shadows, snow, sensor saturation, hazy observations (based on atmospheric opacity), and lack of aerosol optical depth information. Two major discoveries are: 1) that filtering saturated and hazy pixels is helpful to reduce noise in the time series, although the impact may vary across different continents; 2) the atmospheric opacity band needs to be used with caution because many images are removed when no value is given in this band, when many of those observations are usable. The results provide guidance on when and where time series analysis is feasible, which will benefit many users of Landsat data.

Extension of period maps by polyhedral fans

Kato and Usui developed a theory of partial compactifications for quotients of period domains D by arithmetic groups Γ, in an attempt to generalize the toroidal compactifications of Ash-Mumford-Rapoport-Tai to non-classical cases. Their partial compactifications, which aim to fully compactify the images of period maps, rely on the choice of a fan which is strongly compatible with Γ. In particular, they conjectured the existence of a complete fan, which would serve to simultaneously compactify all period maps of a given type.In this article, we briefly review the theory, and construct a fan which compactifies the image of a period map arising from a particular two-parameter family of Calabi-Yau threefolds studied by Hosono and Takagi, with Hodge numbers (1,2,2,1). On the other hand, we disprove the existence of complete fans in some general cases, including the (1,2,2,1) case.

On the Image of the Period Map for Polarized Hyperkähler Manifolds

Abstract The moduli space for polarized hyperkähler manifolds of ${\textrm {K3}^{[m]}}$-type or ${\textrm {Kum}}_m$-type with a given polarization type is not necessarily connected, which is a phenomenon that only happens for $m$ large. The period map restricted to each connected component gives an open embedding into the period domain, and the complement of the image is a finite union of Heegner divisors. We give a simplified formula for the number of connected components, as well as a simplified criterion to enumerate the Heegner divisors in the complement. In particular, we show that the image of the period map may be different when restricted to different components of the moduli space.

Deformed WZW models and Hodge theory. Part I

We investigate a relationship between a particular class of two-dimensional integrable non-linear σ-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the λ-deformed G/G model and show that a special class of solutions to its equations of motion precisely describes a one-parameter variation of Hodge structures. We find that this special class is obtained by identifying the group-valued field of the σ-model with the Weil operator of the Hodge structure. In this way, the study of strings on classifying spaces of Hodge structures suggests an interesting connection between the broad field of integrable models and the mathematical study of period mappings.

Power distribution of oscillations in the atmosphere of a plage region

Context. Joint observations of the Atacama Large Millimeter/Submillimeter Array (ALMA) with other solar observatories can provide a wealth of opportunities for understanding the coupling between different layers of the solar atmosphere. Aims. We present a statistical analysis of the power distribution of oscillations in a plage region in active region NOAA AR12651, which was observed jointly with ALMA, the Interface Region Imaging Spectrograph (IRIS), and the Solar Dynamics Observatory (SDO). Methods. We employ coordinated ALMA Band 6 (1.25 mm) brightness temperature maps, IRIS slit-jaw images in the 2796 Å passband, and observations in six passbands (1600 Å, 304 Å, 131 Å, 171 Å, 193 Å, and 211 Å) from the Atmospheric Imaging Assembly (AIA) on board SDO. We perform Lomb-Scargle transforms to study the distribution of oscillation power by means of dominant period maps and power maps. We study the spatial association of oscillations through the atmosphere, with a focus on the correlation of the power distribution of ALMA oscillations with others. Results. We do not observe any significant association of ALMA oscillations with IRIS and AIA oscillations. While the global behavior of the dominant ALMA oscillations shows a similarity with that of the transition region and coronal passbands of AIA, the ALMA dominant period maps and power maps do not show any correlation with those from the other passbands. The spatial distribution of dominant periods and power in different period intervals of ALMA oscillations is uncorrelated with those of any other passbands. Conclusions. We speculate that the non-association of ALMA oscillations with those of IRIS and AIA is due to significant variations in the height of formation of the millimeter continuum observed by ALMA. Additionally, the fact that ALMA directly maps the brightness temperature, in contrast to the intensity observations by IRIS and AIA, can result in the very different intrinsic nature of the ALMA oscillations compared to the IRIS and AIA oscillations.

Stable specific torsion length and periodic mapping classes

We show that for any periodic mapping class, there is some power which maps a nonseparating, simple closed curve to a distinct, disjoint nonseparating curve. As an application of this result, we introduce the notion of stable specific torsion length of a group element and show that the stable specific torsion length of a Dehn twist is bounded above by six.

Morphological evolution of Indus shelf region under the influence of hydrodynamic conditions in 20th century

Indus shelf region, located offshore of the Indus delta, is characterized by several unique and diversified features with dynamic potential of expansion and regression.The growth of this subaqueous part of Indus Delta is the result of the enormous amount of sediments discharge from the Indus River since the Oligocene period. Intervention in the natural flow of the Indus River System (IRS) in the 20th century, due to water diversion and water storage activities on the IRS has created many changes on the continental shelf and shelf-slope in the offshore Indus Delta. The available data of sediment discharge from the Kotri barrage and other previous studies provide information that sediment discharge in natural waterflow conditions before the half of the 20th century was more than 250 million (106) tones per year, but after the construction of canals, barrages and dams in upstream area of the IRS, a gradual declining trend was occurred in the flow of water and sediment discharge.Morphological changes those occurred over the shelf of delta in the 20th century have been evaluated using geoinformatic approach. Two bathymetry maps of the 19th and 20th centuries were used in view to determine the temporal difference on the continental shelf. Ten cross-sections were drawn on both the bathymetry maps in northeast-southwest direction. Profiles from the cross-section of both periods have been developed to analyze the temporal variation on the continental shelf of the offshore Indus Delta. Sediment accumulation was found from 1895 to 1995 on the western edge of the shelf and erosional activities on some places were also noted from the eastern profiles of the continental shelf. Low depth near the coast observed from the map of later period indicates the process of accretion activities near the shore. General trend shows morphologically changes in the shelf region.

Normal generators for mapping class groups are abundant

We provide a simple criterion for an element of the mapping class group of a closed surface to be a normal generator for the mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the genus is at least 3. We also give many examples of pseudo-Anosov normal generators, answering a question of D. D. Long. In fact we show that every pseudo-Anosov mapping class with stretch factor less than \sqrt{2} is a normal generator. Even more, we give pseudo-Anosov normal generators with arbitrarily large stretch factors and arbitrarily large translation lengths on the curve graph, disproving a conjecture of Ivanov.

On conjectures of Hovey–Strickland and Chai

We prove the height two case of a conjecture of Hovey and Strickland that provides a K(n)-local analogue of the Hopkins–Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai. We then use the Gross–Hopkins period map to verify Chai’s Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations for Morava E-theory is coherent, and that every finitely generated Morava module can be realized by a K(n)-local spectrum as long as 2p-2>n^2+n. Finally, we deduce consequences of our results for descent of Balmer spectra.

Translation surfaces and periods of meromorphic differentials

Let S $S$ be an oriented surface of genus g $g$ and n $n$ punctures. The periods of any meromorphic differential on S $S$ , with respect to a choice of complex structure, determine a representation χ : Γ g , n → C $\chi :\Gamma _{g,n} \rightarrow \mathbb {C}$ where Γ g , n $\Gamma _{g,n}$ is the first homology group of S $S$ . We characterise the representations that thus arise, that is, lie in the image of the period map Per : Ω M g , n → Hom ( Γ g , n , C ) $\textsf {Per}:\Omega \mathcal {M}_{g,n}\rightarrow \textsf {Hom}(\Gamma _{g,n}, {\mathbb {C}})$ . This generalises a classical result of Haupt in the holomorphic case. Moreover, we determine the image of this period map when restricted to any stratum of meromorphic differentials, having prescribed orders of zeros and poles. Our proofs are geometric, as they aim to construct a translation structure on S $S$ with the prescribed holonomy χ $\chi$ . Along the way, we describe a connection with the Hurwitz problem concerning the existence of branched covers with prescribed branching data.

Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity

In this paper, we consider nonautonomous second order difference equations of the form xn+1=F(n,xn,xn−1), where F is p-periodic in its first component, non-decreasing in its second component and non-increasing in its third component. The map F is referred to as periodic of mixed monotonicity, which broadens the notion of maps of mixed monotonicity. We introduce the concept of artificial cycles, and we develop the embedding technique to tackle periodicity and globally attracting cycles in periodic 2-dimensional maps of mixed monotonicity. We present a result on globally attracting cycles and illustrate its application to periodic systems. The first application is a periodic rational difference equation of second order, and the second application is a population model with periodic stocking. In both cases, we prove the existence of a globally attracting cycle.

Resilient Responses to Urban Wetland Loss: Experiences from Port Harcourt Municipality

Wetlands globally contribute to valuable ecosystem services to both natural species habitat and human tourist attractions in any location including those found in Port Harcourt Municipality. Wetlands are also beneficial and significant serving as breeding regions for wildlife and safe spaces for sea creatures, support a diversity of species and provide some climate restraining components, characteristic of any natural habitat. This study highlights some resilient responses residents put up in the aftermath of wetland reclamation and conversion in neighbourhoods. The study aims to ascertain the environmental and physical challenges of wetland loss on the wetland dwellers and subsequently identify resilient paradigms adopted to cope with such associated stress. Forty-one wetland settlements were identified within the Port Harcourt municipality and three out of those settlements were chosen purposively. A total of 293 questionnaires were distributed and SPSS was used to analyse the data. ERDAS Imagine 2014 version was used to show spatial changes between the years 1986 to 2000, and 2000 to 2016. The study shows that from 1986 to 2000, Port Harcourt municipality lost a total of 1,255,500m2. This translates to a 5% loss with an average rate of 89,678.57m2 per annum. Between 2000 and 2016, the rate of loss was 108,956.25m2 per annum, and approximately 7.69% of wetlands totalling 1,743,300m2 were lost to urbanisation and other activities. The result indicates that some of the challenges of wetland loss include flooding, poor refuse disposal system, and unplanned settlements. Indigenous knowledge, social capital and symbolic power are some of the resilient responses displayed by the vulnerable population to build resilience capacities. The study recommends periodic mapping of all wetlands and an effective development control framework to monitor incursions into existing wetlands.

The spectral p-adic Jacquet–Langlands correspondence and a question of Serre

We show that the completed Hecke algebra of $p$-adic modular forms is isomorphic to the completed Hecke algebra of continuous $p$-adic automorphic forms for the units of the quaternion algebra ramified at $p$ and $\infty$. This gives an affirmative answer to a question posed by Serre in a 1987 letter to Tate. The proof is geometric, and lifts a mod $p$ argument due to Serre: we evaluate modular forms by identifying a quaternionic double-coset with a fiber of the Hodge–Tate period map, and extend functions off of the double-coset using fake Hasse invariants. In particular, this gives a new proof, independent of the classical Jacquet–Langlands correspondence, that Galois representations can be attached to classical and $p$-adic quaternionic eigenforms.