@article{10208,
abstract = {It is practical to collect a huge amount of movement data and environmental context information along with the health signals of individuals because there is the emergence of new generations of positioning and tracking technologies and rapid advancements of health sensors. The study of the relations between these datasets and their sequence similarity analysis is of interest to many applications such as health monitoring and recommender systems. However, entering all movement parameters and health signals can lead to the complexity of the problem and an increase in its computational load. In this situation, dimension reduction techniques can be used to avoid consideration of simultaneous dependent parameters in the process of similarity measurement of the trajectories. The present study provides a framework, named CaDRAW, to use spatial–temporal data and movement parameters along with independent context information in the process of measuring the similarity of trajectories. In this regard, the omission of dependent movement characteristic signals is conducted by using an unsupervised feature selection dimension reduction technique. To evaluate the effectiveness of the proposed framework, it was applied to a real contextualized movement and related health signal datasets of individuals. The results indicated the capability of the proposed framework in measuring the similarity and in decreasing the characteristic signals in such a way that the similarity results -before and after reduction of dependent characteristic signals- have small differences. The mean differences between the obtained results before and after reducing the dimension were 0.029 and 0.023 for the round path, respectively.},
author = {Goudarzi, Samira and Sharif, Mohammad and Karimipour, Farid},
issn = {1868-5145},
journal = {Journal of Ambient Intelligence and Humanized Computing},
keywords = {general computer science},
publisher = {Springer Nature},
title = {{A context-aware dimension reduction framework for trajectory and health signal analyses}},
doi = {10.1007/s12652-021-03569-z},
year = {2021},
}
@inproceedings{9253,
abstract = {In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics.},
author = {Heiler, Georg and Reisch, Tobias and Hurt, Jan and Forghani, Mohammad and Omani, Aida and Hanbury, Allan and Karimipour, Farid},
booktitle = {2020 IEEE International Conference on Big Data},
isbn = {9781728162515},
location = {Atlanta, GA, United States},
pages = {3123--3132},
publisher = {IEEE},
title = {{Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic}},
doi = {10.1109/bigdata50022.2020.9378374},
year = {2021},
}
@article{9317,
abstract = {Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.},
author = {Edelsbrunner, Herbert and Osang, Georg F},
issn = {1432-0444},
journal = {Discrete and Computational Geometry},
pages = {1296–1313},
publisher = {Springer Nature},
title = {{The multi-cover persistence of Euclidean balls}},
doi = {10.1007/s00454-021-00281-9},
volume = {65},
year = {2021},
}
@article{9602,
abstract = {An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.
A key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees.},
author = {Pach, János and Tomon, István},
issn = {0095-8956},
journal = {Journal of Combinatorial Theory. Series B},
pages = {21--37},
publisher = {Elsevier},
title = {{Erdős-Hajnal-type results for monotone paths}},
doi = {10.1016/j.jctb.2021.05.004},
volume = {151},
year = {2021},
}
@article{9649,
abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently
fine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.},
author = {Boissonnat, Jean-Daniel and Wintraecken, Mathijs},
issn = {1615-3383},
journal = {Foundations of Computational Mathematics },
publisher = {Springer Nature},
title = {{The topological correctness of PL approximations of isomanifolds}},
doi = {10.1007/s10208-021-09520-0},
year = {2021},
}
@article{10071,
author = {Adams, Henry and Kourimska, Hana and Heiss, Teresa and Percival, Sarah and Ziegelmeier, Lori},
issn = {1088-9477},
journal = {Notices of the American Mathematical Society},
number = {9},
pages = {1511--1514},
publisher = {American Mathematical Society},
title = {{How to tutorial-a-thon}},
doi = {10.1090/noti2349},
volume = {68},
year = {2021},
}
@article{10413,
abstract = {Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces.},
author = {Dikranjan, Dikran and Giordano Bruno, Anna and Künzi, Hans Peter and Zava, Nicolò and Toller, Daniele},
issn = {0166-8641},
journal = {Topology and its Applications},
publisher = {Elsevier},
title = {{Generalized quasi-metric semilattices}},
doi = {10.1016/j.topol.2021.107916},
year = {2021},
}
@article{10608,
abstract = {We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.},
author = {Weighill, Thomas and Yamauchi, Takamitsu and Zava, Nicolò},
issn = {2199-6768},
journal = {European Journal of Mathematics},
publisher = {Springer Nature},
title = {{Coarse infinite-dimensionality of hyperspaces of finite subsets}},
doi = {10.1007/s40879-021-00515-3},
year = {2021},
}
@inproceedings{10367,
abstract = {How information is created, shared and consumed has changed rapidly in recent decades, in part thanks to new social platforms and technologies on the web. With ever-larger amounts of unstructured and limited labels, organizing and reconciling information from different sources and modalities is a central challenge in machine learning. This cutting-edge tutorial aims to introduce the multimodal entailment task, which can be useful for detecting semantic alignments when a single modality alone does not suffice for a whole content understanding. Starting with a brief overview of natural language processing, computer vision, structured data and neural graph learning, we lay the foundations for the multimodal sections to follow. We then discuss recent multimodal learning literature covering visual, audio and language streams, and explore case studies focusing on tasks which require fine-grained understanding of visual and linguistic semantics question answering, veracity and hatred classification. Finally, we introduce a new dataset for recognizing multimodal entailment, exploring it in a hands-on collaborative section. Overall, this tutorial gives an overview of multimodal learning, introduces a multimodal entailment dataset, and encourages future research in the topic.},
author = {Ilharco, Cesar and Shirazi, Afsaneh and Gopalan, Arjun and Nagrani, Arsha and Bratanič, Blaž and Bregler, Chris and Liu, Christina and Ferreira, Felipe and Barcik, Gabriek and Ilharco, Gabriel and Osang, Georg F and Bulian, Jannis and Frank, Jared and Smaira, Lucas and Cao, Qin and Marino, Ricardo and Patel, Roma and Leung, Thomas and Imbrasaite, Vaiva},
booktitle = {59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts},
isbn = {9-781-9540-8557-2},
location = {Bangkok, Thailand},
pages = {29--30},
publisher = {Association for Computational Linguistics},
title = {{Recognizing multimodal entailment}},
doi = {10.18653/v1/2021.acl-tutorials.6},
year = {2021},
}
@phdthesis{7944,
abstract = {This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.
For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.
In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.},
author = {Masárová, Zuzana},
isbn = {978-3-99078-005-3},
issn = {2663-337X},
keywords = {reconfiguration, reconfiguration graph, triangulations, flip, constrained triangulations, shellability, piecewise-linear balls, token swapping, trees, coloured weighted token swapping},
pages = {160},
publisher = {IST Austria},
title = {{Reconfiguration problems}},
doi = {10.15479/AT:ISTA:7944},
year = {2020},
}