Defining the We-map Reference Frames and Providing Mathematical Expressions for Transformation Relations

We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate systems is critical,and exploring reference frames is essential in direction and coordinate systems.Despite its significance,existing research on We-map lacks specific solutions for the exploration of reference frames is indispensable for the establishment of accurate direction and coordinate systems.In this paper,we endeavor to address this gap by elucidating the significance of We-map reference frames,defining them with mathematical constraints,summarizing their nature and characteristics,deriving their transformation relationships and representing them through mathematical formulars and equations.Our work contributes to the fundamental theory of We-map and provides valuable systems and support for the mathematical foundation of We-map,map production,and platform development.Ultimately,this research serves to advance the development of We-map.

THE RELATION BETWEEN EVOLUTION OF SPATIAL WORKING MEMORY FUNCTION AND OF MORPHOLOGY OF THE DORSOLATERAL PREFRONTAL CORTEX AMONG THE RHESUS MONKEY, SLOW LORIS AND TREE SHREW

The relation between evolution of spatial working memory function and of morphology of the dorsolateral prefrontal cortex among the rhesus monkey (Macaca mulatta), the slow loris (Nycticebus coucang) and the tree shrew (Tupaia belangen chinensis) were reported in present paper. The results read as follows: In the DR performance with training, the rhesus monkeys and slow lorises could reach a criterion of 90% correct response at 1.1 ± 3.2 seconds, and 3.8±0.4 seconds delay interval, respectively, by 1000 training trails. The tree shrews failed to reach the criterion of 90% correct response even at 0 seconds delay interval by 1000 training trails. If a delay interval was tested in one session (30 trails) only, doing the DR performamce without training, the rhesus monkeys reached a correct of 80% or higher in each session at 0, 1, 2, 3, 4, and 5 seconds delay, respectively. The percent correct in each session of the slow lorises showed no differences from the rhesus monkeys at 0, 1, 2, 3, and 4 seconds delay. However, when the delay interval was increased to 5 seconds, the percent correct of the DR performance declined to 70% or lower in the slow lorises. In the tree shrews the percent correct in each session reached to 70% or lower at 0, 1, 2, 3, 4, and 5 seconds delay interval, respectively. The morphological studies revealed that the size of the prefrontal cortex increased, and the structure got complex in the course of the evolution in primates. It is suggested that the relation of evolution between the spatial working memory function and anatomy in the prefrontal cortex might be significant among the three species, both the development of morphology and that of the spatial working memory function in the dorsolateral prefrontal cortex are later than other regions of cerebral cortex in phylogenetic evolution course.

Fuzzy topological relations between fuzzy spatial objects

Fuzziness is an internal property of spatial objects.How to model fuzziness of a spatial object is a main task of next generation GIS.This paper proposes basic fuzzy spatial object types based on fuzzy topology.These object types are the natural extension of current nonfuzzy spatial object types.A fuzzy cell complex structure is defined for modeling fuzzy regions,lines and points.Furthermore,fuzzy topological relations between these fuzzy spatial objects are formalized based on the 9intersection approach.This model can be implemented for GIS applications due to its scientific theory basis.

Matching spatial relation graphs using a constrained partial permutation strategy

A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.

Fundamental Theories of Spatial Similarity Relations in Multi-scale Map Spaces

Similarity relation is one of the spatial relations in the community of geographic information science and cartography.It is widely used in the retrieval of spatial databases, the recognition of spatial objects from images, and the description of spatial features on maps.However, little achievements have been made for it by far.In this paper, spatial similarity relation was put forward with the introduction of automated map generalization in the construction of multi-scale map databases;then the definition of spatial similarity relations was presented based on set theory, the concept of spatial similarity degree was given, and the characteristics of spatial similarity were discussed in detail, in-cluding reflexivity, symmetry, non-transitivity, self-similarity in multi-scale spaces, and scale-dependence.Finally a classification system for spatial similarity relations in multi-scale map spaces was addressed.This research may be useful to automated map generalization, spatial similarity retrieval and spatial reasoning.

Hierarchical Detailed Description for Spatial Direction Relations

Direction relation is an important spatial relation. Descriptions and representations for direction relations have different levels of detail because of the varying dimensions of spatial objects and different scales of the embedding spaces. Based on a direction- relation matrix, the hierarchical frame of spatial direction relations which partitions direction relations orderly and thoroughly is built. Interior direction relations are used to perfect the representation of direction relations and the binary-encoding idea is creatively applied to construct an interior detailed matrix describing multiple interior direction relations by a uniform matrix. The model integrates topological information into the description model for direction relations, which will lay the foundations of spatial compositive reasoning.

Definitions of Natural-Language Spatial Relations: Combining Topology and Directions

Because SQL for querying data from spatial databa se s is ineffective, the query based on natural or visual language becomes an attra ctive research field gradually. However, how to define and represent natural lan guages related to spatial data are still gigantic problems. Because existing mod els of direction relations can’t describe by use of some common concepts. First of all, detailed direction relations are proposed to describe the directions re lated to the interior of spatial objects, such as "east part of a region","ea st boundary of a region", and so on. Secondly, by integrating the detailed dire ctions with exterior direction relations and topological relations, several NLSR s are defined, such as "a road goes across the east part of a lake", "a river goes along the east boundary of a province", etc. Finally, based on the NLSRs abovementioned, a natural spatial query language (NSQL) is formed to retrieve da ta from spatial databases.

Spatial Relation Resolution and Spatial Relation Abstraction

This paper attempts toregard spatial relation transformationas an important process in map gener-alization. The spatial relation generali-zation can be divided into the compo-nents of abstraction: topology, dis-tance and orientation. The concept‘ spatial relation resolution' is intro-duced to describe the constraints ofrelative spatial relation. On the basisof nine intersection models, the cardi-nal direction models and the iso-dis-tance-relation models, this paper givesthree sorts of relation resolution repre-sentations for topological, distance andorientation relation, respectively. Twomapping implementations in map gen-eralization is discussed.

DEALING WITH SPATIAL RELATIONS FOR SPATIAL OBJECTS WITH RANDOMNESS IN GIS

To design retrieval algorithm of spatial relations for spatial objects with randomness in GIS,this paper builds up the membership functions based on set theory idea,used for determination of topological spatial relations between random objects,such as between point and point,point and line or polygon,which provides theoretical basis for retrieving spatial relations between certain and random objects.Finally,this paper interprets detailed methods and steps of realizing them by means of some simple examples under the GIS’s environment.

Impact of high-speed railway construction on spatial relationships in the Guanzhong Plain urban agglomeration

The Guanzhong Plain urban agglomeration is a response to the Belt and Road Initiative in Northwest China that aims to promote regional development.The direct impact of high-speed railway construction is to shorten the spatial-temporal distance among regions,improve the accessibility of regional transportation,and promote socioeconomic linkages.From the perspective of accessibility,this study analyzes the impact of high-speed railway construction on the spatial pattems and county-level economic relationships of the Guanzhong Plain urban agglom-eration.The results show that the construction of high-speed railway significantly improves regional accessibility,increases the potential for urban economic development,and gradually narrows the gaps in economic potential among cities.The construction of high-speed railway has increased the intensity of extenal economic relations among numerous counties in the Guanzhong Plain urban agglomeration,and most of the areas with increased connections are located in the direction of routes extension.The development of the internal economic network of the Guanzhong Plain urban agglomeration is unbalanced,and a complex network is gradually emerging with a few large cities at the core,but the construction of high-speed railway is changing the struicture of the economic network.In general,a certain degree of intrinsic coupling exists between regional accessibility change and the evolution of economic relations caused by high-speed railway,reflecting the requirements of the regional overall development strategy.

Spatial Interaction Network Analysis of Crude Oil Trade Relations between Countries along the Belt and Road

Based on the theories and methods of complex network,crude oil trade flows between countries along the Belt and Road(B&R,hereafter)are inserted into the Geo-space of B&R and form a spatial interaction network which takes the countries as nodes and takes the trade relations as edges.The networked mining and evolution analysis can provide important references for the research on trade relations among the B&R countries and the formulation of trade policy.This paper researches and discusses the construction,statistical analysis,top networks and stability of the crude oil trade network between the B&R countries from 2001 to 2020 from the perspectives of Geo-Computation for Social Sciences(GCSS)and spatial interaction.Firstly,evolutions of out-degree,in-degree,out-strength and in-strength of the top 10 countries in the crude oil trade network are computed and analyzed.Secondly,the top network method is used to explore the evolution characteristics of hierarchical structures.And finally,the sequential evolution characteristics of the crude oil trade network stability are analyzed utilizing the network stability measure method based on the trade relationship autocorrelation function.The analysis results show that Russia has the largest out-degree and out-strength,and China has the largest in-degree and in-strength.The crude oil trade volume of the top 10 import and export networks between 2001—2020 accounts for over 90%of the total trade volume of the crude oil trade network,and the proportion remains relatively stable.However,the stability of the network showed strong fluctuations in 2009,2012 and 2014,which may be closely related to major international events in these years,which could furtherly be used to build a correlation model between network volatility and major events.This paper explores how to construct and analyze the spatial interaction network of crude oil trade and can provide references for trade relations research and trade policy formulation of B&R countries.

An Improved Direction Relation Detection Model for Spatial Objects

Direction is a common spatial concept that is used in our daily life. It is frequently used as a selection condition in spatial queries. As a result, it is important for spatial databases to provide a mechanism for modeling and processing direction queries and reasoning. Depending on the direction relation matrix, an inverted direction relation matrix and the concept of direction pre- dominance are proposed to improve the detection of direction relation between objects. Direction predicates of spatial systems are also extended. These techniques can improve the veracity of direction queries and reasoning. Experiments show excellent efficiency and performance in view of direction queries.

A New Type of Phase Transition Based on the Clausius-Clapeyron Relation Involving a Change in Spatial Dimension

Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transitions from dimension of space, n, to dimension of space, (n - 1), and vice versa, from (n - 1) to n -dimensional space. For the former we can calculate a specific release of latent heat, a decrease in entropy, and a change in volume. For the latter, we derive an expression for the absorption of heat, the increase in entropy, and the difference in volume. Total energy is conserved in this transformation process. We apply this model to black-body radiation in the early universe and find that for a transition from n = 4 to (n - 1) = 3, there is an immense decrease in entropy accompanied by a tremendous change in volume, much like condensation. However, unlike condensation, the volume change is not three-dimensional. The volume changes from V4, a four-dimensional construct, to V3, a three-dimensional entity, which can be considered a subspace of V4. As a specific example of how the equation works, we consider a transition temperature of 3 × 1027 Kelvin, and assume, furthermore, that the latent heat release in three-dimensional space is 1.8 × 1094 Joules. We find that for this transition, the internal energy densities, the entropy densities, and the volumes assume the following values (photons only). In four-dimensional space, we obtain, u4 = 1.15×10125 J? m-4, s4 = 4.81×1097 J? m-4? K-1, and V4 = 2.14×10-31 m4. In three-dimensional space, we have u3 = 6.13×1094 J? m-3, s3 = 2.72×1067 J? m-3? K-1, and V3 = 0.267 m3. The subscripts 3 and 4 refer to three-dimensional and four-dimensional quantities, respectively. We speculate, based on the tremendous change in volume, the explosive release of latent heat, and the magnitudes of the other quantities calculated, that this type of transition might have a connection to inflation. With this work, we prove that space, in and of itself, has an inherent energy content. This is so because giving up space releases latent heat, and buying space costs latent heat, which we can quantify. This is in addition to the energy contained within that space due to radiation. We can determine the specific amount of heat exchanged in transitioning between different spatial dimensions with our generalized Clausius-Clapeyron equation.

Are Black Holes 4-D Spatial Balls Filled with Black Body Radiation? Generalization of the Stefan-Boltzmann Law and Young-Laplace Relation for Spatial Radiative Transfers

This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.

A STUDY ON CELLULAR AUTOMATA BASED ON RELATIONAL DATABASES AND SPATIO-TE MPORAL SIMULATIONS OF CULTURE DIFFUSION

This paper presents a development o f the extended Cellular Automata9CA),based on relational databases(RDB),to model dynamic interactions amon g spatial objects.The integration o f Geographical Information System(GIS)and CA has the great advantage of simu lationg geographical processes.But standard CA has some restrictions i n cellular shape and neighbourhood and neighbour rules,which restrict the CA’ s ability to simulate complex,real world environ-ments.This paper discusses a cell’ s spatialrelationbasedonthe spatialobject’ s geometricalandmon -geometricalc haracter-istics,and extends the cell’ s neighbour definition,and considers that the cell’ s neighbour lies in the forms of not on ly spa-tial adjacency but also attribute co rrelation.This paper then puts forw ard that spatial relations between t wo different cells can be divided into three types,including spatial adjacency,neighbour hood and complicated separation.Ba sed on tradition-al ideas,it is impossible to settle CA’ s restrictions completely.RDB -based CA is an academic experiment,in which some fields ard desighed to describe the essential information needed to define and select a cell’ s neighbour.The culture innovation diffusion system has mul tiple forms of space diffusion and in herited characteristics that the RD B -based CA is capable of simulating more effectiv ely.Finally this paper details a successful case study on the diffusion o f fashion wear trends.Compared to the original CA,the RDB -based CA is a more natural and efficient representation of human k nowl-edge over space,and is an effective t ol in simulation complex systems that have multiple forms of spatial diff usion.

A new measure for evaluating spatially related properties of traffic information credibility

With the wide applications of sensor network technology in traffic information acquisition systems,a new measure will be quite necessary to evaluate spatially related properties of traffic information credibility.The heterogeneity of spatial distribution of information credibility from sensor networks is analyzed and a new measure,information credibility function(ICF),is proposed to describe this heterogeneity.Three possible functional forms of sensor ICF and their corresponding expressions are presented.Then,two feasible operations of spatial superposition of sensor ICFs are discussed.Finally,a numerical example is introduced to show the calibration method of sensor ICF and obtain the spatially related properties of expressway in Beijing.The results show that the sensor ICF of expressway in Beijing possesses a negative exponent property.The traffic information is more abundant at or near the locations of sensor,while with the distance away from the sensor increasing,the traffic information credibility will be declined by an exponential trend.The new measure provides theoretical bases for the optimal locations of traffic sensor networks and the mechanism research of spatial distribution of traffic information credibility.

The Precise Representation Model of Topological Relations of Complex Planar Objects

For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topological content between complex objects into account, this paper presents a model of basic topological relations between line/planar objects, and then in which the basic topological relations and the concept of the overlapping area are leveraged to describe the topological relations of simple planar objects. The definition of traversing of the hole’s boundary and planar with a hole is used to describe the topological relations between complex planar objects. Finally, the five basic topological relationship description modes of complex planar objects are summarized to realize description of the details of topological relations between partitions of complex planar objects.

Multi-dimensional ambiguity function for subarray-based space-time coding radar

Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit element increases.A subarray-based space-time coding(sub-STC)radar is explored to alleviate the range resolution reduction.For the proposed radar configuration,an identical waveform is transmitted and it introduces a small time offset in different subarrays.The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range,Doppler,angle and probing direction.Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage,resolution performance and low sidelobes are also given.Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.

Effect of Neurofeedback on Visual-Spatial Attention in Male Children with Reading Disabilities: An Event-Related Potential Study

Recent studies describe a number of difficulties associated with attention deficit in children with reading disabilities. Information about visual-spatial attention mainly arises from studies using event-related potentials (ERPs) during Posner’s spatial cueing paradigm. This study aims to use neurofeedback with a special protocol for treating children with reading disabilities, and moreo-ver, to evaluate visual-spatial attention ability by means of Posner paradigm task and ERPs. The study was conducted in a single subject design in 20 sessions. Participants were 2 male children, aged between 10 - 12 years old, who completed twelve 30-min neurofeedback sessions. Repeated measurements were performed during the baseline, treatment, and post treatment phases. Results showed some improvement in Posner paradigm parameters (correct response, valid and invalid reaction times). Furthermore, grand average ERPs for both of the participants in each of the four conditions (Valid-right, Invalid-right, Valid-left and Invalid-left) were analyzed. The analysis of P3 component showed a reduction in latency, indicating an improvement in the timing of cognitive processes. In addition, the graphs showed a decrease in amplitude level, which meant easier processing than before.

VTI介质改进声学近似qP波交错网格正演模拟

Alkhalifah提出的声学假设近似令沿TI介质对称轴的qSV波速度近似为0,建立了相应的qP波波动方程并进行了数值模拟,但存在两个不足:一是方程中存在退化的qSV波解,不是纯qP波波动方程;二是方程不适用于ε<δ(ε和δ为Thomsen参数)的介质。为此,在Liang等的工作基础上,将改进声学近似方法的思想引入qP波频散关系和一阶波动方程推导。令qSV波的精确频散关系中的圆频率为0,同时结合椭圆分解,推导了VTI介质纯qP波解耦频散关系,利用改进标量算子的空间域渐近近似建立了VTI介质改进声学近似qP波一阶速度—应力波动方程,采用交错网格有限差分算法实现了基于改进声学近似的VTI介质纯qP波正演模拟。频散关系分析和数值示例表明,基于改进声学近似的qP波一阶波动方程不包含退化qSV波,是纯qP波方程,与弹性波波动方程模拟结果吻合较好,具有较高精度,并且该方程在ε≥δ和ε<δ的VTI介质中均是稳定的,同时也适用于复杂VTI介质。