Primitive Map Research Articles

Stability of Tschirnhausen Bundles

Abstract Let $\alpha \colon X \to Y$ be a general degree $r$ primitive map of nonsingular, irreducible, projective curves over an algebraically closed field of characteristic zero or larger than $r$. We prove that the Tschirnhausen bundle of $\alpha $ is semistable if $g(Y) \geq 1$ and stable if $g(Y) \geq 2$.

The Gauss maps of Demoulin surfaces with conformal coordinates

Demoulin surfaces in real projective $3$-space are investigated. Our result enable us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian $6$-symmetric space.

PolyFit

Raster clip-art images, which consist of distinctly colored regions separated by sharp boundaries typically allow for a clear mental vector interpretation. Converting these images into vector format can facilitate compact lossless storage and enable numerous processing operations. Despite recent progress, existing vectorization methods that target such data frequently produce vectorizations that fail to meet viewer expectations. We present PolyFit , a new clip-art vectorization method that produces vectorizations well aligned with human preferences. Since segmentation of such inputs into regions had been addressed successfully, we specifically focus on fitting piecewise smooth vector curves to the raster input region boundaries, a task prior methods are particularly prone to fail on. While perceptual studies suggest the criteria humans are likely to use during mental boundary vectorization, they provide no guidance as to the exact interaction between them; learning these interactions directly is problematic due to the large size of the solution space. To obtain the desired solution, we first approximate the raster region boundaries with coarse intermediate polygons leveraging a combination of perceptual cues with observations from studies of human preferences. We then use these intermediate polygons as auxiliary inputs for computing piecewise smooth vectorizations of raster inputs. We define a finite set of potential polygon to curve primitive maps, and learn the mapping from the polygons to their best fitting primitive configurations from human annotations, arriving at a compact set of local raster and polygon properties whose combinations reliably predict human-expected primitive choices. We use these primitives to obtain a final globally consistent spline vectorization. Extensive comparative user studies show that our method outperforms state-of-the-art approaches on a wide range of data, where our results are preferred three times as often as those of the closest competitor across multiple types of inputs with various resolutions.

Подходы к картографированию регионального рынка жилья для обеспечения визуализации национального проекта «Жильё и городская среда»

The article shows various ways of mapping the regional residential real estate market, which can be used in the future to visualize the National Project “Housing and Urban Environment”, implemented until 2024. The author demonstrates different types of cartodiagrams. It is shown that the equipment of residential real estate is more convenient to display a petal cartodiagram. Attention is paid to the use of cartodiagram with stroke, the semicircular and mesh cartodiagram. The author gives a significant place in the publication to the method of mapping housing affordability for citizens, as one of the important tasks of the National Project “Housing and Urban Environment” is to create conditions for increasing the level of affordability of residential real estate acquisition. There are 4 availability indicators that can be displayed on the map using special cartograms and the cartogram method. The most successful option, according to the author, is a combination of two techniques for the image of a cartogram on one map. Attention and rather rare means of socio-economic mapping, in particular the pseudoisolines (of isopleth). The author notes that this method is one of the most obvious in mapping the residential real estate market, especially the price situation. The article, by building isoprices, it was clearly shown how to identify the main geographical factors in the pricing of the housing market. Attention is paid to the geoinformation component of the isopleth construction. The algorithm of working with them using the Spatial Analyst module of the ArcView GIS program is shown. According to the author, cartographic research should be completed with the construction of synthetic maps. One example of synthesis in mapping the housing market is a map of its geographical segmentation. Such maps can be supplemented with matrix legends. The author emphasizes the importance of moving away from primitive maps with one or two cartographic methods to complex maps.

Primitives as building blocks for constructing land cover maps

Land cover maps play an integral role in environmental management. However, countries and institutes encounter many challenges with producing timely, efficient, and temporally harmonized updates to their land cover maps. To address these issues we present a modular Regional Land Cover Monitoring System (RLCMS) architecture that is easily customized to create land cover products using primitive map layers. Primitive map layers are a suite of biophysical and end member maps, with land cover primitives representing the raw information needed to make decisions in a dichotomous key for land cover classification. We present best practices to create and assemble primitives from optical satellite using computing technologies, decision tree logic and Monte Carlo simulations to integrate their uncertainties. The concept is presented in the context of a regional land cover map based on a shared regional typology with 18 land cover classes agreed on by stakeholders from Cambodia, Laos PDR, Myanmar, Thailand, and Vietnam. We created annual map and uncertainty layers for the period 2000–2017. We found an overall accuracy of 94% when taking uncertainties into account. RLCMS produces consistent time series products using free long term historical Landsat and MODIS data. The customizable architecture can include a variety of sensors and machine learning algorithms to create primitives and the best suited smoothing can be applied on a primitive level. The system is transferable to all regions around the globe because of its use of publicly available global data (Landsat and MODIS) and easily adaptable architecture that allows for the incorporation of a customizable assembly logic to map different land cover typologies based on the user's landscape monitoring objectives

A new computable sufficient condition for the convergence of subdivision schemes with nonnegative masks

We are interested in nontrivial conditions on the nonnegative masks that guarantee the convergence of the correspondent subdivision schemes. Roughly speaking, a certain convexity of the support of the given mask implies the convergence of the subdivision scheme. Moreover, those conditions are computable. The key of proving our main theorem is to find out an irreducible or primitive mapping on some multi-integer set and to show the uniqueness of this mapping.

Application of fractional-order differentiation in multispectral image fusion

ABSTRACTIn this letter, a novel pansharpening method is proposed using component substitution (CS) framework. In order to inject the spatial details into the low resolution multispectral (MS) bands, the fractional-order differentiation is used. Eight direction masks are superimposed on each other to construct a unique mask. The primitive detail map is calculated using the difference between the panchromatic (PAN) image and a linear combination of the low resolution MS bands. To refine the detail map and better pansharpening, the superimposed mask is convolved with the extracted primitive detail map. Two datasets collected by the WorldView-2 and Pleiades satellites are used to examine the proposed method. Experimental results show that in comparison with the state-of-the-art methods, the proposed method can better provide the spectral and spatial information in the fused product quantitatively and subjectively.

Formal Killing fields for minimal Lagrangian surfaces in complex space forms

The differential system for minimal Lagrangian surfaces in a 2 C -dimensional, non-flat, complex space form is an elliptic integrable system defined on the Grassmann bundle of oriented Lagrangian 2-planes. This is a 6-symmetric space associated with the Lie group SL ( 3 , C ) , and the minimal Lagrangian surfaces arise as the primitive maps. Utilizing this property, we derive the inductive differential algebraic formulas for a pair of the formal loop algebra s l ( 3 , C ) [ [ λ ] ] -valued canonical formal Killing fields. For applications, (a) we give a complete classification of the (pseudo) Jacobi fields for the minimal Lagrangian system, (b) we obtain an infinite sequence of conservation laws from the components of the canonical formal Killing fields.

Alternative interpretation of the 1D-box solution and the Bargmann theorem

Primitive mapping of 2D fractal spaces yields a formulation of the Schro¨ dinger equation and endows its solutions and the respective 3D objects with specific geometric images. In particular, it is shown that the simplest 1D-box solution comprising no parameters of particles motion can be interpreted as a 2D inhomogeneous string oscillating on a real-imaginary fractal surface or as a 3D static spindle with a harmonically distributed mass spectrum. The description of an inertially moving similar object is obtained using a Bargmann-type theorem applied to the Bohm equations, and, as their exact solution, a fractal function containing explicit kinematic terms.

서로 다른 프리미티브 집합을 사용하는 CAD 시스템 사이에 선박 의장 설계 데이터의 교환

Different CAD systems are used in ship outfitting design on different usage and purpose. Therefore, data exchanges between CAD systems are required from different formats. For data exchange, boundary representation standard formats such as IGES and ISO 10303 (STEP) are widely used. However, they present only B-rep representation. Because of different CAD systems have their own geometry format, data exchanges with design intend are difficult. Especially, Tribon and PDMS use primitives for express their geometry in ship outfitting design. However, Tribon primitives are represented their parameter by values that are non-parametric. Therefore, data size of catalogue library is bigger than different CAD system using parametric primitive representation. And that system has difficulty on data reprocessing. To solve that problem, we discuss about shape DB which contains design parameters of primitive for exchange Tribon primitives. And geometry data exchange between Tribon and Shape Database that defines based on PDMS scheme are specified using primitive mapping that can represent design intend.

Light-weight kernel instrumentation framework using dynamic binary translation

Mobile platforms such as Android and iOS, which are based on typical operating systems, have been widely adopted in various computing devices from smart phones even to smart TVs. Along with this, the necessity of kernel instrumentation framework has also grown up for efficient development and debugging of a kernel itself and its components. Although the existing approaches are providing some information about the kernel state including physical register value and primitive memory map, it is hard for the developers to understand and exploit the information. Moreover, the excessive analysis overhead in the existing approach makes them impractical to be used in real systems. Meanwhile, there have been a few studies on analyzing the user-level applications using dynamic binary translation and they are now widely used. In this paper, by extending this idea of dynamic binary translation for user-level applications to the kernel, we propose a new dynamic kernel instrumentation framework. Our framework focuses on the modules such as device drivers, rather than the kernel itself, since the modules comprise a large portion of OS development. Because of the frequent execution of kernel modules, the dynamic kernel instrumentation framework should guarantee the quality of the translated target code. However, costly optimizations to achieve high execution performance are rather harmful to the overall performance. Therefore, in order to improve performance of both translations, we suggest light-weight translator based on pseudo-machine instruction representation and tabular-base translation instead of typical intermediate representation. We implement our framework on Linux system, and our experimental evaluations show that it could quite effectively instrument the target with nominal overhead.

Qualitative part-based models in content-based image retrieval

A qualitative, volumetric part-based model is proposed to improve the categorical invariance and viewpoint invariance in content-based image retrieval, and a novel two-step part-categorization method is presented to build it. The method consists first in transforming parts extracted from a segmented contour primitive map and then categorizing the transformed parts using interpretation rules. The first step allows noisy extracted parts to be transformed to the domain of a simple classifier. The second step computes features of the transformed parts for categorization. Content-based image retrieval experiments using real images of complex multi-part objects confirm that a model built from the categorized parts improves both the categorical invariance and the viewpoint invariance. It does so by directly addressing the fundamental limits of low-level models.

Associative Cones and Integrable System

We identify R 7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S 6 . It is known that a cone over a surface M in S 6 is an associative submanifold of R 7 if and only if M is almost complex in S 6 . In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S 6 is the equation for primitive maps as- sociated to the 6-symmetric space G2/T 2 , and use this to explain some of the known results. Moreover, the equation for S 1 -symmetric almost complex curves in S 6 is the periodic Toda lattice associated to G2, and a discussion of periodic solutions is given.

Domain theory and differential calculus (functions of one variable)

We introduce a domain-theoretic framework for differential calculus. We define the set of primitive maps as well as the derivative of an interval-valued Scott continuous function on the domain of intervals, and show that they are dually related, providing an extension of the classical duality of differentiation and integration as in the fundamental theorem of calculus. It is shown that, for locally Lipschitz functions of a real variable, the domain-theoretic derivative coincides with the Clarke's derivative. We then construct a domain for differentiable real-valued functions of a real variable by pairing consistent information about the function and information about its derivative. The set of classical functions, locally Lipschitz functions and more generally of all continuous functions. We prove that consistency of function information and derivative information is decidable on rational step functions, which shows that our domain can be given an effective structure. We thus obtain a data type for differential calculus. As an immediate application, we present a domain-theoretic formulation of Picard's theorem, which provides a data type for solving differential equations.

A GIS-based Spatial Pattern Analysis Model for eco-region mapping and characterization

Growing concerns about global climate change, biodiversity maintenance, natural resources conservation, and long-term ecosystem sustainability have been responsible for the transformation of traditional single resource management approaches into integrated ecosystem management models. Eco-regions are large ecosystems of regional extent that contain smaller ecosystems of similar response potential and resource production capabilities. They can be used as a geographical framework for organizing and reporting resource information, setting bioecological recovery criteria, extrapolating site-level management, and monitoring global change. The objective of this research is to develop a quantitative, multivariate regionalization model that is capable of delineating eco-regions at multiple levels from remotely sensed information and other environmental and natural resources spatial data. The Spatial Pattern Analysis Model developed in this study uses a region-growing algorithm to generate spatially contiguous regions from primitive polygonal land units. The algorithm merges the most similar pair of neighbouring units at each iteration, based on satisfying certain similarity criteria until all units are grouped into one. This model was utilized to develop an eco-region map of Nebraska with three hierarchical levels. In the mapping process, the STATSGO data set was used to build the primitive map units. Environmental parameters included in the model were multi-temporal AVHRR data, soil rooting depth, organic matter content, available water capacity, and long-term annual averages of water balance and growing degree day totals. Development of the model provides a new and useful approach to eco-region mapping for resource managers and researchers. The method is automated and efficient, reduces the judgement biases and uncertainty of manual analyses, and can be replicated for other regions or for the regionalization of other themes.

Development of transferable interaction models for water. I. Prominent features of the water dimer potential energy surface

We present an analysis of the morphology of the water dimer potential energy surface (PES) obtained from ab initio electronic structure calculations and perform a quantitative comparison with the results from various water potentials. In order to characterize the morphology of the PES we have obtained minimum energy paths (MEPs) as a function of the intermolecular O–O separation by performing constrained optimizations under various symmetries (Cs, Ci, C2, and C2v). These constitute a primitive map of the dimer PES and aid in providing an account for some of its salient features such as the energetic stabilization of “doubly hydrogen-bonded” configurations for R(O–O)<2.66 Å. Among the various interaction potentials that are examined, it is found that the family of anisotropic site potential (ASP) models agrees better with the ab initio results in reproducing the geometries along the symmetry-constrained MEPs. It is demonstrated that the models that produce closest agreement with the morphology of the ab initio PES, tend to better reproduce the experimental data for the second virial coefficients. We finally comment on the functional forms of simple water models and discuss how effects such as charge overlap can be incorporated into such models.

Harmonic superconformal maps of surfaces in Hn

The class of harmonic superconformal maps from Riemann surfaces into real hyperbolic spaces is considered and harmonic sequences are constructed for these maps. They are used to obtain a rigidity result for such maps and to construct primitive lifts into an auxiliary flag space F m . It is also shown that superconformal harmonic maps into H 2 m and H 2 m−1 are locally described by 2D-affine Toda fields associated to the pair ( so(2m+1,C),σ) , where σ is the involution determined by the non-compact real form so(1,2m) . Applying the Adler–Kostant–Symes integration scheme to appropriate loop algebras we construct finite type primitive maps ψ:H 2→ F m , and harmonic superconformal maps f: H 2→ H 2 m and hence finite type Toda fields.

The Research Pyramid: A Framework for Accounting Information Systems Research

This paper extends Sowa's (1997) Meaning Triangle to develop a framework for accounting information systems (AIS) research—the Research Pyramid. This framework identifies relationships between objects in economic reality, people's concepts of economic reality, symbols used to record and represent economic reality, and the resultant accounting information systems that capture and present data about economic reality. The Research Pyramid has two major uses. First, the paper illustrates how the Research Pyramid can be used to identify new research questions to extend existing research streams. To be used in this manner, existing AIS research is classified along each of the edges of the Research Pyramid. Once an area of the literature has been analyzed, the edges that have not been studied extensively reveal potential primitive mappings for future exploration. Second, each primitive mapping is evaluated to identify which of four research methodologies (design science, field studies, survey research, and laboratory experiments) are likely techniques for use in future studies. This analysis can help researchers with strong methodological training to identify new, interesting questions to be answered that capitalize on their research strengths. As such, the Research Pyramid is a tool to characterize existing AIS research, identify areas for future exploration, and provide guidance on appropriate methodologies to apply.

A Smart-Scanning Analog VLSI Visual-Attention System

We have implemented a hardware model of selective visual attention within the neuromorphic, analog VLSI paradigm. The system includes a highly-parallel winner-take-all selection with excitatory and inhibitory influences. The selection specifies positions of attention based on an array of intensity levels, which comprise a primitive saliency map. The excitation and inhibition control the strategy for shifts of attention from one position to the next. The combination of these fundamental building blocks demonstrates emergent properties that can be observed in real time due to the parallel hardware implementation. The system behaves as a smart-scanning sensor array. The basic characteristics of the scanning pattern are controlled by setting a number of analog parameters. In this paper we describe the system, focusing on the role that inhibition plays in the redirection of attention. We show experimental results from one-dimensional implementations of the hardware model. Analysis that explains the expected behavior for the two-element mode of operation is presented. The theoretical predictions are compared to experimental results.

On non-linear extensions of the Perron-Frobenius theorem

The note provides bounds for eigenvalues of non-negative, homogeneous mappings, which need not be linear. It also gives a simple proof of the result, that repeated iterations of a primitive mapping take any semipositive vector to the positive eigenvector.