Analytic Maps Research Articles

Efficient Optimization Design Method of PMSLM Based on Deep Adaptive Ridge Regression With Embedded Analytical Mapping Function

To improve the thrust performance of permanent magnet synchronous linear motor (PMSLM), novel deep adaptive ridge regression with embedded analytical mapping function (EAMF-RR) is proposed to calculate the thrust performance of PMSLM quickly and accurately, and combined with the EAMF-RR, a whale optimization algorithm (WOA) is introduced to optimize the PMSLM structure. First, the PMSLM's thrust is analyzed by the analytical modeling (AM) to determine the variation range of structural design parameters. Based on the variation range, a finite-element sample database is established for the EAMF-RR. Then, EAMF derived from AM, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbor algorithm, and WOA are integrated into RR to establish deep adaptive EAMF-RR model. Comparative simulation experiments conducted by using another two machine learning methods, i.e., extreme learning machine and weighted random forest, confirm the superiority of the EAMF-RR. Finally, WOA is reused to optimize the thrust performance of PMSLM, and prototype experiments prove the effectiveness of the proposed optimization method.

Proposals for the use of graphical models in urban climatic maps

We suggest applying the chorematic methodology to the processes and issues addressed by the urban climatic mapping framework, i.e., the interdisciplinary discussion and analysis of thematic data, the production of analytic maps, and the creation of recommendation maps to advise urban planners. After introducing the method, its theoretical basis, and its process, we discuss its fitness and present the possibility of its application in this thematic context. We then suggest a first series of applications, for diurnal heat stress and nocturnal urban heat island analysis, as an example and basis for further discussions, based on recent work in the Toulouse agglomeration. We also offer graphical models to express recommendations concerning urban climate issues in Toulouse. The process used the choremes table expanded with dynamic models, according to the multi-step method proposed by H. Théry (1988). The produced models are now entering a test phase to discuss the method with urban planners.

Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models

We propose a scheme to construct predictive models for Hamiltonian matrices in atomic orbital representation from ab initio data as a function of atomic and bond environments. The scheme goes beyond conventional tight binding descriptions as it represents the ab initio model to full order, rather than in two-centre or three-centre approximations. We achieve this by introducing an extension to the atomic cluster expansion (ACE) descriptor that represents Hamiltonian matrix blocks that transform equivariantly with respect to the full rotation group. The approach produces analytical linear models for the Hamiltonian and overlap matrices. Through an application to aluminium, we demonstrate that it is possible to train models from a handful of structures computed with density functional theory, and apply them to produce accurate predictions for the electronic structure. The model generalises well and is able to predict defects accurately from only bulk training data.

Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space

We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.

Community engaged tick surveillance and tickMAP as a public health tool to track the emergence of ticks and tick-borne diseases in New York.

A community engaged passive surveillance program was utilized to acquire ticks and associated information throughout New York state. Ticks were speciated and screened for several tick-borne pathogens. Of these ticks, only I. scapularis was commonly infected with pathogens of human relevance, including B. burgdorferi, B. miyamotoi, A. phagocytophilum, B. microti, and Powassan virus. In addition, the geographic and temporal distribution of tick species and pathogens was determined. This enabled the construction of a powerful visual analytical mapping tool, tickMAP to track the emergence of ticks and tick-borne pathogens in real-time. The public can use this tool to identify hot-spots of disease emergence, clinicians for supportive evidence during differential diagnosis, and researchers to better understand factors influencing the emergence of ticks and tick-borne diseases in New York. Overall, we have created a community-engaged tick surveillance program and an interactive visual analytical tickMAP that other regions could emulate to provide real-time tracking and an early warning for the emergence of tick-borne diseases.

Theoretical principles of spatial analysis of the history of administrative-territorial division

The article considers the theoretical aspects of spatial and spatio-temporal analysis of changes in the administrative-territorial division, its history. It is shown that despite the presence of a significant number of publications on the history of administrative-territorial division, the complex issue of its detailed spatial analysis has not been resolved. The main focus of the author of the article is on diachronic analysis. Levels of analysis are highlighted depending on which object from the history of territorial division is analyzed (one-dimensional linear objects – administrative boundaries, dynamic polygonal objects – administrative units, objects denoting changes, or arbitrary territories and territories with an identical history of administrative affiliation, within which the history of specific objects in the history of administrative-territorial division is summarized with the calculation of the corresponding aggregative indicator). The difference between the study of change as part of the history of specific objects of territorial organization and the study of change as individual spatial objects is described. The principles of allocation of areas of spatial changes, their varieties are described. For each level of analysis, the types of objects that can be units of mapping on analytical or synthetic maps from the history of administrative-territorial division are proposed and described in detail. Typical operations on space-time data on the history of territorial division are considered. Examples of specific indicators on the history of administrative-territorial division that can be calculated for the described objects are given. Differences in the calculation of similar in meaning indicators for objects of different types are described. Particular attention is paid to indicators-aggregates of the history of administrative-territorial division within individual territories. Classifications of such indicators are given. In particular, local aggregates, focal aggregates and aggregates of dynamic objects are distinguished. Examples of the analysis of the administrative reform of 2020 at the district level within the Dnipropetrovsk region are given. The features of comparative analysis of individual states or periods for different objects of change are briefly described.

Spatial differentiation of Stryi raion of Lviv oblast: challenges for development

The article raises the issue of comprehensive human-geographical research of administrative-territorial units formed as a result of reforming the administrative-territorial structure of Ukraine. The human-geographical meaning of the concept of "administrative district capacity" as its ability to function effectively in accordance with natural, demographic and economic potentials is introduced and revealed. Using a cartographic method, a series of analytical maps elaborated, which revealed significant spatial heterogeneity in terms of territorial communities of Stryi Raion (district) in terms of providing by land resources, population and settlement density, level of urbanization, general budget revenues per unit area and per capita, taфability index. Based on the Methodology for the Formation of Capable Territorial Communities (2020), groups of territorial communities with high (3.9 – 4.6) and medium (3.2 – 3.8) levels of capacity identified at the studied area. Elaboration of the approved strategies for the development of territorial communities made it possible to summarize the priority areas of economic development of the district: tourism and recreational, transport and logistical, agrarian, industrial. Clustering is proposed as an effective process of territorial organization of the economy of Stryi Raion. The need to transform the city-forming functions of the former district centers (Zhydachiv, Mykolaiv, Skole) into new economic realities is emphasized.

Abstract No. 9 Evaluating global interventional radiology services to improve maternal morbidity and mortality: geographic information system mapping of postpartum hemorrhage and interventional radiology availability in Kenya

Postpartum hemorrhage (PPH) is the leading preventable cause of maternal illness and death globally, accounting for up to 20% of deaths in developing regions. Improving availability and awareness of interventional radiology (IR) services such as uterine artery embolization may improve maternal morbidity and mortality in these regions. The purpose of this study was to evaluate PPH and IR services landscapes in Kenya using geographic information systems (GIS) analytic mapping.

Quasiconformal extension of integral transforms of analytic and harmonic mappings

In this article, we prove a criterion for quasiconformal extension of the integral transforms of analytic functions defined in the unit disk of the complex plane. Thereafter, we prove a sufficient condition for quasiconformal extensibility of sense-preserving harmonic mappings defined in the unit disk and applying this result, we obtain criteria for the quasiconformal extension of various types of integral transforms that are defined for sense-preserving harmonic mappings. We also study the stability of the quasiconformal extension of sense-preserving harmonic mappings.

Multivariate Analysis of Geological Data for Regional Studies of Geodiversity

In Norway, a landscape map exists which gives the opportunity to collect data in landscape units for further analysis. This study covers parts of Norway and Sweden, so the landscape map was extended into Sweden to form a unified landscape structure. A collection of geological and terrain data within landscape units can serve as a tool to describe the geodiversity profile of the units, study their geographical distribution and analyse similarities and dissimilarities between them. We collected geological and terrain data for an area covering large parts of southern Norway and Sweden. The data were collected as attributes in landscape polygons. The data were then analysed using multivariate techniques (Principle component analyses) where the first four axes of variation were definable. The first axis is a terrain axis, the second a bedrock unit axis, the third a bedrock diversity axis and the fourth a soil/sediment axis. In total, the four gradients answer for 54.9% of the total variation in the material. Links are found between the terrain data and geological units, but these links are relatively weak. The four gradients represent a step-less model of the geodiversity profile of the landscape areas but are dependent on the quality and scale of the input data. Norwegian and Swedish data had to be harmonised in order to be analysed together; however, because of this they ended up having a coarser resolution than desired, both spatially and scientifically. The stepless model was clustered to form 16 geodiversity profile groups for easy comparison and regional overview. The procedure can serve as a baseline for more detailed and field-based studies of geodiversity profiles, and give the opportunity to make analytical maps through simple overlay techniques and to compare areas with each other with respect to their geodiversity profile. This can be carried out both alone and in a wider landscape setting.

A new averaging-extrapolation method for quasi-periodic frequency refinement

In a recent work, we presented an averaging-extrapolation approach for the numerical computation of frequencies and amplitudes of a discrete-time quasi-periodic signal. This approach assumes analyticity of the signal and a Diophantine frequency vector. Given an approximation to one of the frequencies and a sufficiently large number of iterates of the signal, the main outcome of the method is a refined approximation to the frequency. The crucial aspect of this method consists in building an appropriate complex signal which, by the geometrical implications of its construction, is referred to as an unfolded signal. The projection of the unfolded signal on the unit circle defines a quasi-periodic signal of the circle whose rotation frequency is the target frequency. This allows to refine the target frequency by adapting a previously developed method for computing, with great accuracy, Diophantine rotation numbers of analytic circle maps. Both the unfolding and refinement processes require computing appropriate weighted averages of the iterates and performing Richardson’s extrapolation. In the present work, we reformulate this averaging-extrapolation approach to frequency refinement. This leads to a simpler method that completely avoids the unfolding process but that is capable of producing accurate values for frequencies and amplitudes at a reasonable computational cost, which is mostly independent of the number of basic frequencies of the signal.

Highly Sensitive Detection of the Antidepressant Fluoxetine With an Extended Gate Field Effect Transistor

Fluoxetine (FL) is one of the selective serotonin reuptake inhibitors, which is used as an anti-depressant, as well as anti-panic drug. In this work, a sensor for label-free recognition of trace amounts of FL is introduced, which is based on an extended gate field-effect transistor (EGFET). This sensor enables the detection and accurate measurement of FL concentrations over wide dynamic range. The sensing part of the device is a Pt electrode covered by a sensitive polyvinyl chloride (PVC) membrane. The functionalized Pt electrode acting as an extended gate of the EGFET, is connected to the internal gate of a MOSFET transducer. The sensing element of the PVC membrane is the insoluble ion-pair of FL cation and tetraphenylborate anion. The sensor performance for detection of FL was characterized in different ionic strengths of the matrix solution. Then, the sensor capability to operate in physiological phosphate-buffered saline (PBS) was assessed, where the sensor indicated two linear dynamic ranges of its response, with different sensitivities in 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−11</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> M and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> M ranges. Also the calculated detection limit for the sensor was <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.63\times 10^{-12}$ </tex-math></inline-formula> M. Moreover, the selectivity of the sensor was examined and validated in the presence of Citalopram, which is another anti-depressant drug with a similar structure to FL. We proposed a comprehensive analytical mapping of current sensitivity in all working regimes of the EGFET, providing a guide to the design of optimized sensors in any integrated systems of interest. Finally, the sensor was successfully exploited to assay citalopram in its pharmaceutical formulation.

The dual tree of a fold map germ from to

Let $f\colon (\mathbb {R}^{3},0)\to (\mathbb {R}^{4},0)$ be an analytic map germ with isolated instability. Its link is a stable map which is obtained by taking the intersection of the image of $f$ with a small enough sphere $S^{3}_\epsilon$ centred at the origin in $\mathbb {R}^{4}$. If $f$ is of fold type, we define a tree, that we call dual tree, that contains all the topological information of the link and we prove that in this case it is a complete topological invariant. As an application we give a procedure to obtain normal forms for any topological class of fold type.

Gevrey estimates for asymptotic expansions of Tori in weakly dissipative systems* *Both authors have been supported by NSF Grant DMS 1800241.

We consider a singular perturbation for a family of analytic symplectic maps of the annulus possessing a KAM torus. The perturbation introduces dissipation and contains an adjustable parameter. By choosing the adjustable parameter, one can ensure that the torus persists under perturbation. Such models are common in celestial mechanics. In field theory, the adjustable parameter is called the counterterm and in celestial mechanics, the drift. It is known that there are formal expansions in powers of the perturbation both for the quasi-periodic solution and the counterterm. We prove that the asymptotic expansions for the quasiperiodic solutions and the counterterm satisfy Gevrey estimates. That is, the nth term of the expansion is bounded by a power of n!. The Gevrey class (the power of n!) depends only on the Diophantine condition of the frequency and the order of the friction coefficient in powers of the perturbative parameter. The method of proof we introduce may be of interest beyond the problem considered here. We consider a modified Newton method in a space of power expansions. As is custumary in KAM theory, each step of the method is estimated in a smaller domain. In contrast with the KAM results, the domains where we control the Newton method shrink very fast and the Newton method does not prove that the solutions are analytic. On the other hand, by examining carefully the process, we can obtain estimates on the coefficients of the expansions and conclude the series are Gevrey.

Thrust Performance Improvement of PMSLM Based on Lasso Regression With Embedded Analytical Model

AbstractTo solve the problem that both analytical model and finite element model are difficult to give consideration to the calculation accuracy and efficiency at the same time in motor optimization work, a novel Lasso regression with the embedded analytical model, called EAM-LR, is proposed to quickly and accurately calculate the thrust performance of the permanent magnet synchronous linear motor (PMSLM) in this paper. First, the thrust performances of PMSLM are analyzed by the analytical model (AM) to determine the variation range of structural design parameters. Based on the variation range, a finite-element sample database is established. Then, combined with the finite-element sample database, the analytical mapping functions derived from AM, are integrated into Lasso regression to establish EAM-LR. The accuracy of EAM-LR was verified by comparison with AM, traditional lasso regression, and well-known extreme learning machine. Finally, combined with the EAM-LR, the chaotic golden section algorithm (CGA) is introduced to search the optimal structure parameters of PMSLM, and the control simulation and prototype experiment prove the effectiveness of the proposed method.

Map of the Libyan conflict in the post- Gaddafi period – Analytical study for the period between the National Congress elections until Fajr Libya Operation (2012- 2015): خارطة الصراع الليبي في فترة ما بعد القذافي – دراسة تحليلية لفترة ما بين انتخابات المؤتمر الوطني حتى عملية فجر ليبيا (2012- 2015)

After the fall of the Gaddafi regime, the Libyans tried to restructure the state, although they were able to change the regime in months, rebuilding the state was not that easy. One of the most prominent challenges for officials in that period was to address the social division left by the internal war between the February revolutionaries and the Gaddafi regime. In this study, the Libyan conflict in the post- Gaddafi period is analyzed, by presenting an analytical map for the period between the elections of the Transitional National Congress, which is the first legislative council in Libya after the revolution, until Fajr Libya Operation, which is the beginning of the first civil war in the post- Gaddafi era. The study was built according to the qualitative approach, in an attempt to understand and analyze the events based on academic literature and reports. As a result, the study concluded that the Libyan society did not recover from the wounds of the civil war that is experienced, and the absence of transitional justice was one of the direct causes in the emergence of the Libyan conflict because it was not among the priorities of Libyan officials at that stage. In addition to the mentality that prevailed the revolutionaries after their overthrow of the Gaddafi regime, which translated into actions that contributed to an increase in social division.

Book Review: Singularities of mappings: The local behaviour of smooth and complex analytic mappings

Book Review: Singularities of mappings: The local behaviour of smooth and complex analytic mappings

THE THOM CONDITION

In this note we explain the notion of the Thom condition for the Whitney stratifications of a complex analytic map. We give a question P. Deligne and indicate a possible way to answer it.

Formal Gevrey solutions: in analytic germs—for higher order holomorphic PDEs

We consider a family of holomorphic PDEs whose singular locus is given by the zero set of an analytic map P with P(0)=0. Our goal is to establish conditions for the existence and uniqueness of formal power series solutions and to determine their divergence rate. In fact, we prove that the solution is Gevrey in P, giving new information on divergency while compared to the classical Gevrey classes. If P is not singular at 0, we also provide Poincaré conditions to recover convergent solutions. Our strategy is to extend the dimension and lift the given PDE to a problem where results of singular PDEs can be applied. Finally, examples where the Gevrey class in P is optimal are included.

Curie-Point Depths, Geothermal Gradients and Sub-Surface Heat Flow Estimation from Spectral Analysis of High-Resolution Aeromagnetic Data over Gongola Basin and Its Environs, Northeastern Nigeria

Geothermal energy resources have been established globally to be among the sustainable and environmentally harmless means of energy generation. Curie-point depths (CPD), temperature gradients, and heat flow data over the study area were computed using a spectral analysis method in order to have a preliminary view of the geothermal implications (prospect) of the current area. Aeromagnetic data acquired by the Nigerian Geological Survey Agency (NGSA) in the year 2009 was used for the research. The results showed the minimum, maximum, and the average CPD values as 8.18 km, 31.48 km, and 13.0 km, respectively. The minimum, maximum and average thermal gradients obtained were 18.42 °C/km, 70.91 °C/km, and 50.2 °C/km, respectively. The heat flow data obtained ranged from 33.15 mW/m2 to 177.28 mW/m2, with an average value of 110.65 mW/m2. Locations depicting shallow CPDs anomalies (Alkaleri, Darazo, Dukku, Misau, Wuyo, Deba, and Tula), also showed conformity with high heat flow areas. As such, they are regarded as areas of promising geothermal prospects and are recommended for further detailed investigation. Locations depicting a high magnetic susceptibility contrast from a generated analytic signal map, as well as high temperature gradients, high heat flow, and shallow CPDs are attributed to crustal thinning along the sedimentary basin and magmatic intrusions along basement areas, respectively. The magnetic depth to the basement calculated for the study area using the source parameter imaging (SPI) method ranges from 0.610 km to 3.055 km. The present study has provided an insight on preliminary information, regarding new areas of possible geothermal prospects for further detailed investigation.