Related papers: A Topological Representation for Taking Cities as …
Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more…
Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
Several natural and artificial structures and systems are somehow optimized for performing specific functionalities. The structure and topology of cities is no exception, as it is critically important to ensure effective access to the…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this…
In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 U.S. cities and a few more from elsewhere of different sizes. It is found that all the…
Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…
Easy and intuitive navigability is of central importance in cities. The actual scale-free networking of urban street networks in their topological space, where navigation information is encoded by mapping roads to nodes and junctions to…
Many complex networks demonstrate a phenomenon of striking degree correlations, i.e., a node tends to link to other nodes with similar (or dissimilar) degrees. From the perspective of degree correlations, this paper attempts to characterize…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how…
In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of…
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
Kevin Lynch proposed a theory of the image of the city identifying five elements that make the city legible or imageable. The resulting mental map of the city was conventionally derived through some qualitative processes, relying on…