4,259 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    A Look at Financial Dependencies by Means of Econophysics and Financial Economics

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    This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets' dependencies, especially correlational studies, which in our opinion are beneficial for researchers in both fields. In econophysics, these dependencies can be modeled to describe financial markets as evolving complex networks. In particular we show that a useful way to describe dependencies is by means of information filtering networks that are able to retrieve relevant and meaningful information in complex financial data sets. In financial economics these dependencies can describe asset comovement and spill-overs. In particular, several models are presented that show how network and factor model approaches are related to modeling of multivariate volatility and asset returns respectively. Finally, we sketch out how these studies can inspire future research and how they contribute to support researchers in both fields to find a better and a stronger common language

    Space-Query Tradeoffs in Range Subgraph Counting and Listing

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    This paper initializes the study of range subgraph counting and range subgraph listing, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as opposed to all, vertices. In the first problem, there is an undirected graph G where each vertex carries a real-valued attribute. Given an interval q and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced by the vertices whose attributes fall in q. The second problem has the same setup except that a query needs to enumerate (rather than count) those occurrences with a small delay. In both problems, our goal is to understand the tradeoff between space usage and query cost, or more specifically: (i) given a target on query efficiency, how much pre-computed information about G must we store? (ii) Or conversely, given a budget on space usage, what is the best query time we can hope for? We establish a suite of upper- and lower-bound results on such tradeoffs for various query patterns

    The success probability in Levine's hat problem, and independent sets in graphs

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    Lionel Levine's hat challenge has tt players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are chosen, but not after. Each player sees all hats except for those on her own head. They then proceed to simultaneously try and each pick a black hat from their respective stacks. They are proclaimed successful only if they are all correct. Levine's conjecture is that the success probability tends to zero when the number of players grows. We prove that this success probability is strictly decreasing in the number of players, and present some connections to problems in graph theory: relating the size of the largest independent set in a graph and in a random induced subgraph of it, and bounding the size of a set of vertices intersecting every maximum-size independent set in a graph.Comment: arXiv admin note: substantial text overlap with arXiv:2103.01541, arXiv:2103.0599

    Dynamic scene understanding: Pedestrian tracking from aerial devices.

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    Multiple Object Tracking (MOT) is the problem that involves following the trajectory of multiple objects in a sequence, generally a video. Pedestrians are among the most interesting subjects to track and recognize for many purposes such as surveillance, and safety. In the recent years, Unmanned Aerial Vehicles (UAV’s) have been viewed as a viable option for monitoring public areas, as they provide a low-cost method of data collection while covering large and difficult-to-reach areas. In this thesis, we present an online pedestrian tracking and re-identification from aerial devices framework. This framework is based on learning a compact directional statistic distribution (von-Mises-Fisher distribution) for each person ID using a deep convolutional neural network. The distribution characteristics are trained to be invariant to clothes appearances and to transformations. In real world scenarios, during deployment, new pedestrian and objects can appear in the scene and the model should detect them as Out Of Distribution (OOD). Thus, our frameworks also includes an OOD detection adopted from [16] called Virtual Outlier Synthetic (VOS), that detects OOD based on synthesising virtual outlier in the embedding space in an online manner. To validate, analyze and compare our approach, we use a large real benchmark data that contain detection tracking and identity annotations. These targets are captured at different viewing angles, different places, and different times by a ”DJI Phantom 4” drone. We validate the effectiveness of the proposed framework by evaluating their detection, tracking and long term identification performance as well as classification performance between In Distribution (ID) and OOD. We show that the the proposed methods in the framework can learn models that achieve their objectives

    Asymptotics of stochastic learning in structured networks

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    Subgroup discovery for structured target concepts

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    The main object of study in this thesis is subgroup discovery, a theoretical framework for finding subgroups in data—i.e., named sub-populations— whose behaviour with respect to a specified target concept is exceptional when compared to the rest of the dataset. This is a powerful tool that conveys crucial information to a human audience, but despite past advances has been limited to simple target concepts. In this work we propose algorithms that bring this framework to novel application domains. We introduce the concept of representative subgroups, which we use not only to ensure the fairness of a sub-population with regard to a sensitive trait, such as race or gender, but also to go beyond known trends in the data. For entities with additional relational information that can be encoded as a graph, we introduce a novel measure of robust connectedness which improves on established alternative measures of density; we then provide a method that uses this measure to discover which named sub-populations are more well-connected. Our contributions within subgroup discovery crescent with the introduction of kernelised subgroup discovery: a novel framework that enables the discovery of subgroups on i.i.d. target concepts with virtually any kind of structure. Importantly, our framework additionally provides a concrete and efficient tool that works out-of-the-box without any modification, apart from specifying the Gramian of a positive definite kernel. To use within kernelised subgroup discovery, but also on any other kind of kernel method, we additionally introduce a novel random walk graph kernel. Our kernel allows the fine tuning of the alignment between the vertices of the two compared graphs, during the count of the random walks, while we also propose meaningful structure-aware vertex labels to utilise this new capability. With these contributions we thoroughly extend the applicability of subgroup discovery and ultimately re-define it as a kernel method.Der Hauptgegenstand dieser Arbeit ist die Subgruppenentdeckung (Subgroup Discovery), ein theoretischer Rahmen fĂŒr das Auffinden von Subgruppen in Daten—d. h. benannte Teilpopulationen—deren Verhalten in Bezug auf ein bestimmtes Targetkonzept im Vergleich zum Rest des Datensatzes außergewöhnlich ist. Es handelt sich hierbei um ein leistungsfĂ€higes Instrument, das einem menschlichen Publikum wichtige Informationen vermittelt. Allerdings ist es trotz bisherigen Fortschritte auf einfache Targetkonzepte beschrĂ€nkt. In dieser Arbeit schlagen wir Algorithmen vor, die diesen Rahmen auf neuartige Anwendungsbereiche ĂŒbertragen. Wir fĂŒhren das Konzept der reprĂ€sentativen Untergruppen ein, mit dem wir nicht nur die Fairness einer Teilpopulation in Bezug auf ein sensibles Merkmal wie Rasse oder Geschlecht sicherstellen, sondern auch ĂŒber bekannte Trends in den Daten hinausgehen können. FĂŒr EntitĂ€ten mit zusĂ€tzlicher relationalen Information, die als Graph kodiert werden kann, fĂŒhren wir ein neuartiges Maß fĂŒr robuste Verbundenheit ein, das die etablierten alternativen Dichtemaße verbessert; anschließend stellen wir eine Methode bereit, die dieses Maß verwendet, um herauszufinden, welche benannte Teilpopulationen besser verbunden sind. Unsere BeitrĂ€ge in diesem Rahmen gipfeln in der EinfĂŒhrung der kernelisierten Subgruppenentdeckung: ein neuartiger Rahmen, der die Entdeckung von Subgruppen fĂŒr u.i.v. Targetkonzepten mit praktisch jeder Art von Struktur ermöglicht. Wichtigerweise, unser Rahmen bereitstellt zusĂ€tzlich ein konkretes und effizientes Werkzeug, das ohne jegliche Modifikation funktioniert, abgesehen von der Angabe des Gramian eines positiv definitiven Kernels. FĂŒr den Einsatz innerhalb der kernelisierten Subgruppentdeckung, aber auch fĂŒr jede andere Art von Kernel-Methode, fĂŒhren wir zusĂ€tzlich einen neuartigen Random-Walk-Graph-Kernel ein. Unser Kernel ermöglicht die Feinabstimmung der Ausrichtung zwischen den Eckpunkten der beiden unter-Vergleich-gestelltenen Graphen wĂ€hrend der ZĂ€hlung der Random Walks, wĂ€hrend wir auch sinnvolle strukturbewusste Vertex-Labels vorschlagen, um diese neue FĂ€higkeit zu nutzen. Mit diesen BeitrĂ€gen erweitern wir die Anwendbarkeit der Subgruppentdeckung grĂŒndlich und definieren wir sie im Endeffekt als Kernel-Methode neu

    On the use of senders for minimal Ramsey theory

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    This thesis investigates problems related to extremal and probabilistic graph theory. Our focus lies on the highly dynamic field of Ramsey theory. The foundational result of this field was proved in 1930 by Franck P. Ramsey. It implies that for every integer t and every sufficiently large complete graph Kn, every colouring of the edges of Kn with colours red and blue contains a red copy or a blue copy of Kt. Let q â©Ÿ 2 represent a number of colours, and let H1,..., Hq be graphs. A graph G is said to be q-Ramsey for the tuple (H1,...,Hq) if, for every colouring of the edges of G with colours {1, . . . , q}, there exists a colour i and a monochromatic copy of Hi in colour i. As we often want to understand the structural properties of the collection of graphs that are q-Ramsey for (H1,..., Hq), we restrict our attention to the graphs that are minimal for this property, with respect to subgraph inclusion. Such graphs are said to be q-Ramsey-minimal for (H1,..., Hq). In 1976, Burr, ErdƑs, and LovĂĄsz determined, for every s, t â©Ÿ 3, the smallest minimum degree of a graph G that is 2-Ramsey-minimal for (Ks, Kt). Significant efforts have been dedicated to generalising this result to a higher number of colours, qâ©Ÿ3, starting with the ‘symmetric’ q-tuple (Kt,..., Kt). In this thesis, we improve on the best known bounds for this parameter, providing state-of-the-art bounds in different (q, t)-regimes. These improvements rely on constructions based on finite geometry, which are then used to prove the existence of extremal graphs with certain key properties. Another crucial ingredient in these proofs is the existence of gadget graphs, called signal senders, that were initially developed by Burr, ErdƑs, and LovĂĄsz in 1976 for pairs of complete graphs. Until now, these senders have been shown to exist only in the two-colour setting, when q = 2, or in the symmetric multicolour setting, when H1,..., Hq are pairwise isomorphic. In this thesis, we then construct similar gadgets for all tuples of complete graphs, providing the first known constructions of these tools in the multicolour asymmetric setting. We use these new senders to prove far-reaching generalisations of several classical results in the area
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