Estimating Aggregated Gravitational Attractions by an Algebraic Simplification

Definition:Spatial interaction refers to all cases in which a relationship (a flow of persons, goods, communications, citations, and so on) is observed between pairs of spatial units. Differently from the standard areal or point units often analyzed in spatial science, spatial interaction data are denoted by their bilateral nature. They have an origin and a destination (in the particular case, the two being the same). Such origins and destinations may have observable characteristics. Moreover, each pair of spatial units may be described according to some measures of separation (such as distance) or of commonality (e.g., the presence of a common language). Such descriptors are typically employed in spatial interaction models, the most commonly used analytical framework for modeling flow data. Problems occur when the aforementioned descriptors exhibit correlation between the values of different spatial units or dyads which is due to the spatial configuration of the units themselves (e.g., ...This is an excerpt from the content.

This study aims at developing a data‐driven and bottom‐up spatial statistic method for identifying regions of anomalous spatial interactions (clusters of extremely high‐ or low‐value spatial flows), based on which it creates a spatial flow weights matrix. The method, dubbed flowAMOEBA, upgrades a multidirectional optimum ecotope‐based algorithm (AMOEBA) from areal data to spatial flow data through a proper spatial flow neighborhood definition. The method has the potential to dramatically change the way we study spatial interactions. First, it breaks the convention that spatial interaction data are always collected and modeled between spatial entities of the same granularity, as it delineates the OD region of anomalous spatial interactions, regardless of the size, shape, scale, or administrative level. Second, the method creates an empirical spatial flow weights matrix that can handle network autocorrelation embedded in spatial interaction modeling, thus improving related policy‐making or problem‐solving strategies. flowAMOEBA is tested and demonstrated on a synthetic data set as well as a county‐to‐county migration data set.

In the era of big data, large amounts of detailed spatial interaction data are readily available due to the increasing pervasiveness of location-aware devices and techniques. Such data are often applied in the research of spatial structures, land use characteristics, and human activity regularities. However, visualizing such data on maps is a great challenge. Existing approaches either encounter overlapping and intersection problems, which may cause information loss or distortion, or are unable to present interaction characteristics. Consequently, the functional and positional features of places and human mobility trends are not fully demonstrated. We propose direction-based pattern maps, a new visualization method to display the spatial interaction pattern of every place by aggregating spatial interaction data in cardinal directions. This approach can well represent local interaction characteristics and is applicable to different spatial scales. Owing to regular hexagonal tessellations, it can avoid cluttering problems and maintain a geographical context. A case study using Beijing taxi trip data is conducted to validate the usefulness of our approach.

Spatial statistics: A quantitative geographer’s perspective

This paper addresses the theme of spatial autocorrelation impacting spatial equilibria, and hence an understanding of economic network resilience and vulnerability. It exploits the notion that spatial autocorrelation in the geographic distribution of origin and destination attributes and network autocorrelation in the flows between origins and destinations constitute two spatial autocorrelation components contained in spatial interaction data. It illustrates that a spatial interaction model specification needs to incorporate both components in order to furnish sound implications about associated economic network resilience and vulnerability. Such models also need to undergo sensitivity analyses in terms of changes in geographic scale and resolution. And, it furnishes a novel 3-D visualization of geographic flows, such as journey-to-work trips, in order to achieve a better comprehension of economic network resilience and vulnerability.

This paper proposes a set of specific crossover and mutation operators for the delineation of functional regions through evolutionary computation. We consider a problem of dividing a given territory into local labor market areas based on spatial interaction data. Such areas are defined so that a high degree of inter-regional separation and intra-regional integration - in both cases in terms of commuting flows - exist. A genetic algorithm has been designed based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Additional requirements, typical of any functional regionalization, include the absence of overlapping between delineated regions and an exhaustive coverage of the whole territory (so all basic spatial units must be allocated to one and only one-region). The complex set of restrictions results in conventional operators often generating invalid solutions, impeding or delaying the evolutionary process. This is the reason why an extensive set of operators has been designed that incorporates knowledge about the problem, allowing the evolution of the set of solutions towards the final result.

Spatial scale is a fundamental issue for geographical phenomena because the size of the spatial unit adopted for analysis can have a significant effect on aggregated spatial data and the corresponding analytical results. There exists much research on the scale issue of spatial distribution data while a few has paid attention to the scale effect on spatial interactions. Big geo-data with micro-level individual movements provide an unprecedented opportunity to explore spatial interactions from the bottom up and to understand the scale effect from the perspective of interaction patterns. In this paper, we introduced an empirical framework to explore spatial interaction data across scales. By incorporating two data sets of taxi trajectories in Beijing and Shanghai, we aggregated the taxi O-D trips under multiple regular grids with different cell sizes and analyzed the properties of spatial interactions in three aspects: the statistical distribution, the distance decay mechanism, and the structure pattern. Our research demonstrated the feasibility of analyzing spatial interactions from a multi-scale view and offered a basic empirical framework for future geographical research that is interested in scale and spatial interactions.

In tree-based genetic programming, there is a tendency for the size of the programs to increase from generation to generation, a phenomenon known as bloat. It is standard practice to place some form of control on program size either by limiting the number of nodes or the depth of the program trees, or by adding a component to the fitness function that rewards smaller programs (parsimony pressure). Others have proposed directly simplifying individual programs using algebraic methods. In this paper, we add node-based numerical simplification as a tree pruning criterion to control program size. We investigate the effect of on-line program simplification, both algebraic and numerical, on program size and resource usage. We also investigate the distribution of building blocks within a genetic programming population and how this is changed by using simplification. We show that simplification results in reductions in expected program size, memory use and computation time. We also show that numerical simplification performs at least as well as algebraic simplification, and in some cases will outperform algebraic simplification. We further show that although the two on-line simplification methods destroy some existing building blocks, they effectively generate new more diverse building blocks during evolution, which compensates for the negative effect of disruption of building blocks.

Gravity models, popular for estimating spatial interactions, assume independent spatial interactions from locations to all other locations and, therefore, overlook potential latent multilateral influences in play. This research combines self‐organizing map (SOM) and trajectory analysis to classify patterns of spatial interactions and trace changes in the patterns simultaneously across all locations and decipher the development and dependence of multilateral interactions in space and time. We use international trading among 207 countries from 1900 to 2014 to demonstrate the proposed SOM–trajectory analysis. We create SOMs of annual international trade for all countries, trace each country's changes in trading patterns over 115 years, and compare the trajectories for countries. The combined SOM–trajectory analysis elicits the hidden trading development and geographic influences brought into play. The proposed method is adaptable to other domains of spatial interactions (e.g., immigration) to characterize the temporal patterns of multilateral spatial interactions at locations individually or contextually.

A recent focus in the academic literature on segregation indices is on the development of spatial measures, which make use of information on the relative spatial locations of zones; such measures overcome the spatial location independence of traditional indices, often expressed as the ‘checkerboard problem’. Most spatial measures are based on contiguity weighting - immediate neighbours of a given zone are included in calculations - or distance-decay functions. This chapter considers the restrictions of such approaches and discusses some ways in which distance decay weighting schemes can be adapted to better reflect interactions between people in different areas. The use of data on internal migration as a proxy for the daily interactions between Catholics and Protestants in Northern Ireland is considered, and is shown to depict limited interactions between those on opposite sides of so-called ‘interface areas’. Comparison of results using geographically weighted distance-decay schemes suggests that simple distance-based approaches may, in some cases, have limited practical utility if the derived measures are to be used as a guide to the degree of mixing between members of different population groups.

When investigating healthcare efficiency at the regional level, the problem of interactions between neighbouring locations arises. The health of the population in a given region is related to the healthcare in other areas through a medical tourism, a limited number of highly specialised institutions, competition between institutions, etc. Ignoring these inter-regional links may result in a systematic bias in the efficiency analysis. Similar issues may hinder any regional studies. Hence, the main purpose of this paper is to introduce a new approach to measuring efficiency in regional studies through spatial data envelopment analysis (SDEA). The paper offers a proper mathematical formulation of the new methodology and highlights differences between classic data envelopment analysis (DEA) and the newly developed method. The motivation for seeking a new solution to the problem of spatially adequate assessment of regional efficiency is derived from the literature review and a discussion of the presented theoretical examples. The classic DEA allows for multidimensional analysis of the performance of homogenous independent decision-making units. However, in regional studies, an area where DEA has gained popularity, the assumption of the isolation of decision-making units seems to be unfounded. In the SDEA approach, the region-specific spatial context is incorporated into the analysis via the W matrix and spatial interactions are reflected in the model through spatially weighted inputs and outputs. Therefore, in our paper, we verify the hypothesis that spatial interactions are an indispensable factor of regional efficiency analysis. A study of healthcare efficiency in European regions is presented as an illustration of the utility of the new methodology. Furthermore, we compare the results of the classic DEA approach with those of the SDEA, which is augmented with the spatial equivalents of inputs and outputs. Our results suggest that classic DEA undervalues regional healthcare efficiency by underestimating the region-specific spatial context.2 Researchers may find the introduced SDEA method useful in all space related fields when investigated phenomenon exhibits spatial autocorrelation. In particular, the new approach may deepen the regional efficiency analysis of innovation, development, logistics, tourism, etc.

Interactions between cities play a significant role in the development of metropolitan regions. Although these interactions and their role in the urban growth modelling have already been investigated, there is still room for more studies. In this research, in addition to conventional urban growth factors, spatial interactions between the cities (SIBC) are incorporated into urban growth modelling. This causes directional trends in urban growth (DTUG). Therefore, first the DTUG of each city was measured using a developed indicator based on the history of urban growth that was extracted from satellite images and spatial statistics. The SIBC was then estimated by integrating the DTUG of the cities. Finally, the SIBC and other driving forces, including the physical suitability, accessibility and neighbourhood effects, were integrated using a cellular automata-based model. The accuracy of the model in the Tehran metropolitan region was increased by 6.44% after considering the SIBC. The analysis of the DTUG and SIBC in the Tehran metropolitan region during 1991–2000–2007–2014 revealed specific patterns as the spatial interactions intensified over time and usually peaked in the periphery of the central business districts and intense interactions existed between the metropolises and other major cities. These findings could help urban managers with strategic decision-making in the metropolitan regions and adjust the science and practice relation in this field.

Studies of the pulse charge of lead-acid batteries for PV applications: Part II. Impedance of the positive plate revisited

BackgroundProtein-protein interactions are at the basis of most cellular processes and crucial for many bio-technological applications. During the last few years the development of high-throughput technologies has produced several large-scale protein-protein interaction data sets for various organisms. It is important to develop tools for dissecting their content and analyse the information they embed by data-integration and computational methods.ResultsInteractions can be mediated by the presence of specific features, such as motifs, surface patches and domains. The co-occurrence of these features on proteins interacting with the same protein can indicate mutually exclusive interactions and, therefore, can be used for inferring the involvement of the proteins in common biological processes.We present here a publicly available server that allows the user to investigate protein interaction data in light of other biological information, such as their sequences, presence of specific domains, process and component ontologies. The server can be effectively used to construct a high-confidence set of mutually exclusive interactions by identifying similar features in groups of proteins sharing a common interaction partner. As an example, we describe here the identification of common motifs, function, cellular localization and domains in different datasets of yeast interactions.ConclusionsThe server can be used to analyse user-supplied datasets, it contains pre-processed data for four yeast Protein Protein interaction datasets and the results of their statistical analysis. These show that the presence of common motifs in proteins interacting with the same partner is a valuable source of information, it can be used to investigate the properties of the interacting proteins and provides information that can be effectively integrated with other sources. As more experimental interaction data become available, this tool will become more and more useful to gain a more detailed picture of the interactome.

BackgroundImmunotherapies, in particular immune checkpoint inihibitors (ICI) have led to durable benefit in a subset of head and neck cancers. Understanding and describing the tumour microenvironment (TME) is critical to...