The General Description of Topological Relations based on Node Degree and Euler-number

To solve the disadvantages of high difficulty and complexity in studying the spatial topological relation method on different resolution remote sensing images, this paper proposes a spatial topological relationship model based on GeoSOT, which is one of the global subdivision grids. To express spatial objects on different resolution remote sensing images, this paper introduces the spatial objects subdivision location identification. Then, the model calculates spatial topological relation by comparing location identifications in combined table. At last, test shows that it is feasible to analyze the spatial objects topological relations based on GeoSOT and it has high efficiency operation significantly, especially for complicated spatial objects.

Geospatial datasets are currently constructed, managed, and utilized individually according to the spatial scale of the real world, such as the ground/surface/underground or indoor/outdoor, as well the particular purpose of the geospatial data used for location-based services. In addition, LBS applications use an optimal data model and data format according to their particular purpose, and thus, various datasets exist to represent the same spatial features. Such duplicated geospatial datasets and geographical feature-based GIS data cause serious problems in the financial area, compatibility issues among LBS systems, and data integration problems among the various geospatial datasets generated independently for different systems. We propose a geospatial data fusion model called the topological relation-based data fusion model (TRDFM) using topological relations among spatial objects in order to integrate different geospatial datasets and different data formats. The proposed model is a geospatial data fusion model implemented in a spatial information application and is used to directly provide spatial information-based services without data conversion or exchange of geometric data generated by different data models. The proposed method was developed based on an extension of the AnchorNode concept of IndoorGML. The topological relationships among spatial objects are defined and described based upon the basic concept of IndoorGML. This paper describes the concept of the proposed TRDFM and shows an experimental implementation of the proposed data fusion model using commercial 3D GIS software. Finally, the limitations of this study and areas of future research are summarized.

The topological structures of complex networks have been playing an important role on the epidemic spreading. There has been several studies of pairwise epidemic models on adaptive networks with Poisson distribution, all of which have shown that the rewiring behaviors can lead to complex dynamics numerically or analytically. However, the triples approximation formula under Poisson distribution overlooked the degree of center node of triples which has dramatic effects on the structures. Therefore in this paper, through a new moment closure incorporating the effect of center node's degree, we study how the topological structures of adaptive networks influences epidemic dynamics. The SIS pairwise epidemic model is first closed by the new triple approximation formula, then we transform the model into an equivalent nondimensionalized three dimensional system. By the qualitative theory and the stability theory of ordinary differential equations, the basic reproduction number R0 of the model is obtained, the existence and stabilities of the equilibria are analyzed. Moreover, we prove that the model exhibits transcritical forward bifurcation, backward bifurcation, saddle-node bifurcation and Hopf bifurcation using the methods of bifurcation theory. In addition, by a numerical example, the normal form of Hopf bifurcation and the first Lyapunov coefficient are derived, which show that a stable limit cycle can bifurcate from the endemic equilibrium with larger epidemicity. Our study show that the adaptive behavior can lead to rich dynamics on epidemic transmission, including oscillation and bistability. Finally the numerical simulations which is consistent with the analytical results above are given.

Topological relations are one of the most important aspects in GIS modeling. The topological relations between crisp spatial objects have been well identified. However, the topological relations between fuzzy spatial objects need more investigation. This paper discusses different definitions in fuzzy boundary and their differences and relations. One of the definitions is then selected as the fuzzy boundary for GIS. In order to identify the topological relations between fuzzy spatial objects, three intersection matrices, namely 3*3-intersection matrix, 4*4-intersection matrix and 5*5-intersection matrix, are proposed and formalized in a fuzzy topological space. These matrices are all applicable for identification of topological relations between fuzzy spatial objects. 152 topological relations between two simple fuzzy regions are identified based on the 4×4-intersection approach in R 2 .

Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies. In contrast to most previous works, we avoid making assumptions about which topological properties are important to characterize the AS topology. Our analysis shows that, although matching degree-based properties, the existing AS topology generation models fail to capture the complexity of the local interconnection structure between ASs. Furthermore, we use BGP data from multiple vantage points to show that additional measurement locations significantly affect local structure properties, such as clustering and node centrality. Degree-based properties, however, are not notably affected by additional measurements locations. These observations are particularly valid in the core. The shortcomings of AS topology generation models stems from an underestimation of the complexity of the connectivity in the core caused by inappropriate use of BGP data.

Pattern transformation-invariant schemes for wireless sensor networks based on an edge detection gradient-based mechanism

Objective To explore the topological properties of the brain structural network in patients with neuromyelitis optica spectrum disorder (NMOSD). Methods Diffusion tensor imaging was performed in 41 NMOSD patients (patient group) and 40 age- and sex-matched healthy volunteers (control group) who were admitted to the Department of Neurology, The Third Affiliated Hospital to Sun Yat-sen University from September 2014 to October 2017. The deterministic fiber tracking techniques were used to construct the white matter structural weighted network. Topological properties of the brain structural network were then calculated based on complex graph theory analysis. The 2 groups were compared in terms of global and local parameters of the brain structural network using statistical methods. Results The brain structural networks in both groups exhibited small world properties. Compared with the control group, the global efficiency of the brain structural network in the patient group was significantly decreased and the shortest path length significantly increased (P=0.002, P= 0.002, FDR correction). There were no statistically significant differences between the brain structural networks of the 2 groups in terms of clustering coefficient, the shortest path length on average, value of small world property, average clustering coefficient or local efficiency (P=0.780, P=0.496, P=0.279, P=0.269, P= 0.050, FDR correction). Compared with the control group, the nodal efficiency of the brain structural network of the patient group was significantly decreased in the frontal lobe (bilateral precentral gyrus, middle frontal gyrus of the right orbital part, inferior frontal gyrus of the right opercular part, right rolandic operculum, bilateral median cingulate and paracingulate gyri), parietal lobe (right posterior cingulate gyrus, right superior parietal gyrus, left inferior parietal of angular gyri, right angle gyrus, and right precuneus), temporal lobe (bilateral hippocampus and right parahippocampal gyrus), occipital lobe (left cuneus, left superior occipital gyrus, bilateral middle occipital gyrus, and left inferior occipital gyrus) and subcortical region (right caudate nucleus and right thalamus) (P<0.05, FDR correction). Conclusion There is abnormal connection in brain structural network in NMOSD patients. Key words: Neuromyelitis optica spectrum disorder; Diffusion tensor imaging; Brain structural network; Topological property

The technological progress in the field of artificial intelligence (AI) has brought new opportunities and challenges to the intelligent development and innovative research in fuzzy spatial relations, fuzzy theory is the basic theory of intelligent information processing, and the paper gives a brief analysis of fuzzy calculation method in spatial analysis and spatial relation calculation. In particular, the spatial relations of fuzzy objects are more difficult to express and describe accurately. This paper proposes a method to calculate the topological relations between fuzzy objects with 4-Intersection model and 9-Intersection model, in the analysis of spatial relations, the extension from deterministic entity to uncertain entity is realized with fuzzy set theory, the fuzzy space matrix is constructed, then fuzzy topological relations and fuzzy membership are calculated and output, the model simplifies many complex relations, and it can describe eight topological relations including disjoint, meet, overlap, covers, contains, covered-by, inside and equal. In practical application, the position of spatial objects can be controlled and adjusted according to topological relations. Through analysis of algorithm and fuzzy membership calculation, the model is effective in theory.

The 9+-intersection is an extension of the 9-intersection, which distinguishes the topological relations between various spatial objects by the pattern of a nested matrix. This paper develops a small set of constraints on this matrix, which is applicable to arbitrary pairs of spatial objects in various spaces. Based on this set of universal constraints, the sets of matrix patterns, each representing a candidate for topological relations, are derived for every possible pair of basic objects (points, directed/non-directed line segments, regions, and bodies) embedded in R 1, R 2, R 3, S 1, and S 2. The derived sets of candidates are consistent with the sets of topological relations ever identified, as well as yield the identification of some missing sets of topological relations. Finally, the topological relations between a region and a region with a hole in R 2and S 2are identified to demonstrate the applicability of our approach to deriving topological relations between more complicated objects.

Topological integrity constraints control the topological properties of spatial objects and the validity of their topological relationships in spatial databases. These constraints can be specified by using formal languages such as the spatial extension of the Object Constraint Language (OCL). Spatial OCL allows the expression of topological constraints involving crisp spatial objects. However, topological constraints involving spatial objects with vague shapes (e.g., regions with broad boundaries) are not supported by this language. Shape vagueness requires using appropriate topological operators (e.g., strongly Disjoint, fairly Meet) to specify valid relations between these objects; otherwise, the constraints cannot be respected. This paper addresses the problem of the lack of terminology to express topological constraints involving regions with broad boundaries. We propose an extension of Spatial OCL based on a geometric model for objects with vague shapes and an adverbial approach for topological relations between regions with broad boundaries. This extension of Spatial OCL is then tested on an agricultural database.KeywordsObject Constraint LanguageIntegrity ConstraintSpatial ObjectTopological RelationTopological ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The purpose of this thesis is to give a detail study of the well known Brouwer's fixed point theorem and Nash's equilibrium theorem. Section 1 is an introduction. Notions about triangulations of simplexes are recalled in section 2, the definitions of the affine independence, affne combination, affine hull, convex hull, barycentric coordinate, simplex, face, and triangulation are given and some basic properties of them are listed. In section 3, the definitions of barycenters of simplexes and sequences of ascending simplexes are introduced. After some discussions, the existence of a triangulation, the k-th barycentric subdivision, of a simplex is established, in case k is large enough, the maximum diameter of its members can be arbitrarily small. In section 4, we study some topological properties of convex sets and convex bodies, we see that some special homeomorphisms map convex bodies onto simplexes of suitable dimensions. In section 5, we study the celebrate theorems of Sperner, Knaster-Kuratowski-Mazurkiewicz, and Brouwer in a typical way. In section 6, the definition of noncooperative finite games in normal form is given, notions of the player, pure or mixed strategy, situation, payoff and equilibrium point are introduced with some examples. We see that the fixed points of Nash mappings are exactly the equilibrium points in mixed strategies of the corresponding games.

In this paper we discuss two data models for spatial database systems: the linear data model and the topological data model. Both can be used to model a wide range of applications. The linear data model is particularly suited to model spatial database applications in which exact geometrical information is required and in which this information can be approximated by linear geometrical spatial objects. The topological model on the other hand is suitable for applications in which rather than exact geometrical information the relative position of spatial objects is of importance.We will specify in each case which types of spatial data and spatial databases are under consideration. A semantics for both data models is formally defined in terms of finite representations of spatial databases in the data models. We also present languages to query spatial databases in both models and briefly investigate their expressiveness.KeywordsSpatial DataAffine TransformationSpatial DatabaseSpatial ObjectLinear FigureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Optimization problems that involve discrete variables are exposed to the conflict between being a powerful modeling tool and often being hard to solve. Infinite-dimensional processes, as e.g. described by differential equations, underlying the optimization may lead to the need to solve for distributed discrete control variables. This work analyzes approximation arguments that replace the need for solving the optimization problem by the need for first solving a relaxation and second computing appropriate roundings to regain discrete controls. We provide sufficient conditions on rounding algorithms and their grid refinement strategies that allow to prove approximation of the relaxed controls by the discrete controls in weaker topologies, a feature due to the infinite-dimensional vantage point. If the control-to-state mapping of the underlying process exhibits suitable compactness properties, state vector approximation follows in the norm topology as well as, under additional assumptions, optimality principles of the computed discrete controls. The conditions are verified for representatives of the family of Sum-Up Rounding algorithms. We apply the arguments on different classes of mixed-integer optimization problems that are constrained by partial differential equations. Specifically, we consider discrete control inputs, which are distributed in the time domain, for evolution equations that are governed by a differential operator that generates a strongly continuous semigroup, discrete control inputs, which are distributed in multi-dimensional spatial domains, for elliptic boundary value problems and discrete control inputs, which are distributed in space-time cylinders, for evolution equations that are governed by differential operators such that the corresponding Cauchy problem satisfies maximal parabolic regularity. Furthermore, we apply the arguments outside the scope of partial differential equations to a signal reconstruction problem. Computational results illustrate the findings.

A fundamental problem in computer and communication networks is the wavelength assignment (WA) problem: given a set of routing paths on a network, assign wavelengths (channels) to the paths such that the paths with the same wavelength are edge-disjoint. The optimization problem here is to minimize the number of wavelengths. A popular network topology is a tree of rings. It is known NP-hard to find the minimum number of wavelengths for the WA problem on a tree of rings. Let L be the maximum number of paths on any edge in the network. Then L is a lower bound on the number of wavelengths for the WA problem. We give a polynomial time algorithm which uses at most 3L wavelengths for the WA problem on a tree of rings with node degree at most eight. This improves the previous result of 4L. We also show that some instances of the WA problem require at least 3L wavelengths on a tree of rings, implying that the 3L upper bound is optimal for the worst case instances. In addition, we prove that our algorithm has approximation ratios 2 and 2.5 for a tree of rings with node degrees at most four and six, respectively.

Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in global GIS. However, the most popular models in current use, which are based on the 2D Euclidean space (such as raster), exist some fundamental deficiency in theory for spatial relation reasoning in the spherical digital space (SDS). In this paper, a reasoning method of spatial relations in the SDS based on manifold is approached, in which: (1) the topological definitions, properties, and descriptions of spatial objects in SDS are presented; (2) appropriate operators from set operators (i.e. intersection, difference, difference by, symmetric difference, etc.) are utilized to distinguish the spatial relations between neighboring spatial objects; and (3) the value of the Euler number of symmetric difference is used for the detailed computational results of set operations; In this method, the 8 types basic topological relations between spatial objects in SDS can be distinguished accurately and easily from simple to detailed level for different requirements.