137 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Machine learning applications in search algorithms for gravitational waves from compact binary mergers

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    Gravitational waves from compact binary mergers are now routinely observed by Earth-bound detectors. These observations enable exciting new science, as they have opened a new window to the Universe. However, extracting gravitational-wave signals from the noisy detector data is a challenging problem. The most sensitive search algorithms for compact binary mergers use matched filtering, an algorithm that compares the data with a set of expected template signals. As detectors are upgraded and more sophisticated signal models become available, the number of required templates will increase, which can make some sources computationally prohibitive to search for. The computational cost is of particular concern when low-latency alerts should be issued to maximize the time for electromagnetic follow-up observations. One potential solution to reduce computational requirements that has started to be explored in the last decade is machine learning. However, different proposed deep learning searches target varying parameter spaces and use metrics that are not always comparable to existing literature. Consequently, a clear picture of the capabilities of machine learning searches has been sorely missing. In this thesis, we closely examine the sensitivity of various deep learning gravitational-wave search algorithms and introduce new methods to detect signals from binary black hole and binary neutron star mergers at previously untested statistical confidence levels. By using the sensitive distance as our core metric, we allow for a direct comparison of our algorithms to state-of-the-art search pipelines. As part of this thesis, we organized a global mock data challenge to create a benchmark for machine learning search algorithms targeting compact binaries. This way, the tools developed in this thesis are made available to the greater community by publishing them as open source software. Our studies show that, depending on the parameter space, deep learning gravitational-wave search algorithms are already competitive with current production search pipelines. We also find that strategies developed for traditional searches can be effectively adapted to their machine learning counterparts. In regions where matched filtering becomes computationally expensive, available deep learning algorithms are also limited in their capability. We find reduced sensitivity to long duration signals compared to the excellent results for short-duration binary black hole signals

    Fully Dynamic Maximum Independent Sets of Disks in Polylogarithmic Update Time

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    A fundamental question in computational geometry is for a dynamic collection of geometric objects in Euclidean space, whether it is possible to maintain a maximum independent set in polylogarithmic update time. Already, for a set of intervals, it is known that no dynamic algorithm can maintain an exact maximum independent set with sublinear update time. Therefore, the typical objective is to explore the trade-off between update time and solution size. Substantial efforts have been made in recent years to understand this question for various families of geometric objects, such as intervals, hypercubes, hyperrectangles, and fat objects. We present the first fully dynamic approximation algorithm for disks of arbitrary radii in the plane that maintains a constant-factor approximate maximum independent set in polylogarithmic update time. First, we show that for a fully dynamic set of nn unit disks in the plane, a 1212-approximate maximum independent set can be maintained with worst-case update time O(log⁥2n)O(\log^2 n), and optimal output-sensitive reporting. Moreover, this result generalizes to fat objects of comparable sizes in any fixed dimension dd, where the approximation ratio depends on the dimension and the fatness parameter. Our main result is that for a fully dynamic set of disks of arbitrary radii in the plane, an O(1)O(1)-approximate maximum independent set can be maintained in polylogarithmic expected amortized update time.Comment: Abstract is shortened to meet Arxiv's requirement on the number of character

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Targeted searches for continuous gravitational waves

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    Gravitational waves are a consequence of Albert Einstein’s General theory of relativity, which he put forward in 1916. One hundred years later, in 2015, a gravitational wave signal from two merging black holes was detected by the Advanced LIGO detectors. Now, the Advanced LIGO detectors have recorded about a hundred such signals from the merging of compact objects in binary systems. Rotating neutron stars with a non-axisymmetric distribution of their mass present a perfect candidate for emitting gravitational waves continuously. Such continuous gravitational waves are several orders of magnitude weaker than those emitted by merging binary systems. Not surprisingly, these continuous gravitational wave signals have not yet been detected in the Advanced LIGO data. Efforts to make a detection of such a signal are going on. This thesis presents such a search for continuous gravitational waves. Pulsars are neutron stars from which electromagnetic emissions have been observed, most commonly in the radio wavelength. These observations provide useful information about the neutron star, including its location in the sky and spin parameters. With this knowledge, we search for the continuous gravitational wave from that specific neutron star – thus targeting a source. Such targeted searches probe a small region of the signal parameter space and hence can afford a fully coherent search in data from all observations of the detectors. This makes targeted searches the most sensitive search strategy. In this thesis, we present two different methods to search for continuous gravitational wave signals from pulsars. Using these methods, we target newly discovered, fast-spinning pulsars, a majority of them in binary systems. These pulsars have been targeted for continuous gravitational wave emission for the first time in this work. We do not detect a continuous gravitational wave signal from any of the targets. The non-detection of a signal can be translated into constraints on the mass distortions of the pulsar, parameterized by its ‘ellipticity’. Our constraints on the ellipticities of these pulsars, using data from all the observation runs of Advanced LIGO detectors, are some of the lowest and lie in the regime of astrophysically interesting values for the parameter.Gravitationswellen sind eine direkte Konsequenz der 1916 von Albert Einstein aufge- stellten Allgemeinen RelativitĂ€tstheorie. Hundert Jahre spĂ€ter, im Jahr 2015, wurde ein Gravitationswellensignal von zwei verschmelzenden schwarzen Löchern von den Advanced LIGO-Detektoren detektiert. Inzwischen haben die Detektoren etwa hundert solcher Signale von verschmelzenden kompakten Doppelsternen aufgezeichnet. Rotierende Neutronensterne sind aufgrund der nicht achsensymmetrischen Vertei- lung ihrer Masse ein perfekter Kandidat fĂŒr die kontinuierliche Ausstrahlung von Gravitationswellen. Solche kontinuierlichen Gravitationswellen sind um mehrere Grö- ßenordnungen schwĂ€cher als die, die von verschmelzenden Doppelsternsystemen ausgestrahlt werden. Es ĂŒberrascht deshalb nicht, dass diese kontinuierlichen Gravitati- onswellensignale noch nicht detektiert wurden. Die BemĂŒhungen um den Nachweis eines solchen Signals sind jedoch im Gange. Die vorliegende Arbeit beschĂ€ftigt sich mit der Suche nach kontinuierlichen Gravitationswellen. Pulsare sind Neutronensterne, die im elektromagnetischen Bereich, meist als Radio- wellen, beobachtet werden. Diese Beobachtungen liefern nĂŒtzliche Informationen ĂŒber den Neutronenstern, einschließlich seiner Position am Himmel und seiner Spinpara- meter. Die Informationen können genutzt werden, um gezielt nach der kontinuierli- chen Gravitationswelle eines bestimmten Neutronensterns zu suchen. Solche gezielten Suchen untersuchen lediglich einen kleinen Bereich des Signalparameterraums und ermöglichen dadurch eine vollstĂ€ndig kohĂ€rente Suche in allen Daten der Detektoren. Dies macht die gezielte Suche zur empfindlichsten Suchstrategie. Zwei verschiedene Methoden zur Suche nach kontinuierlichen Gravitationswellen- signalen von Pulsaren werden in dieser Arbeit vorgestellt. Sie zielen auf neu entdeckte, schnell drehende Pulsare ab, von denen sich die meisten in Doppelsternsystemen befinden. Diese Pulsare wurden im Rahmen dieser Arbeit zum ersten Mal auf konti- nuierliche Gravitationswellenemission untersucht. Wir konnten von keinem der Ziele ein kontinuierliches Gravitationswellensignal nachweisen. Die Nichtentdeckung eines Signals kann in Grenzwerte der Deformation eines Pulsars ĂŒbersetzt werden, die durch seine ‘ElliptizitĂ€t’ bestimmt wird. Unsere Grenzwerte fĂŒr die ElliptizitĂ€t dieser Pulsare, die aus Daten aller Beobachtungsreihen der LIGO-Detektoren gewonnen wurden, gehö- ren zu den niedrigsten bisher ermittelten und liegen im Bereich der astrophysikalisch interessanten Werte fĂŒr diesen Parameter

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Symmetric Sparse Boolean Matrix Factorization and Applications

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    In this work, we study a variant of nonnegative matrix factorization where we wish to find a symmetric factorization of a given input matrix into a sparse, Boolean matrix. Formally speaking, given M∈Zm×m\mathbf{M}\in\mathbb{Z}^{m\times m}, we want to find W∈{0,1}m×r\mathbf{W}\in\{0,1\}^{m\times r} such that ∄M−WW⊀∄0\| \mathbf{M} - \mathbf{W}\mathbf{W}^\top \|_0 is minimized among all W\mathbf{W} for which each row is kk-sparse. This question turns out to be closely related to a number of questions like recovering a hypergraph from its line graph, as well as reconstruction attacks for private neural network training. As this problem is hard in the worst-case, we study a natural average-case variant that arises in the context of these reconstruction attacks: M=WW⊀\mathbf{M} = \mathbf{W}\mathbf{W}^{\top} for W\mathbf{W} a random Boolean matrix with kk-sparse rows, and the goal is to recover W\mathbf{W} up to column permutation. Equivalently, this can be thought of as recovering a uniformly random kk-uniform hypergraph from its line graph. Our main result is a polynomial-time algorithm for this problem based on bootstrapping higher-order information about W\mathbf{W} and then decomposing an appropriate tensor. The key ingredient in our analysis, which may be of independent interest, is to show that such a matrix W\mathbf{W} has full column rank with high probability as soon as m=Ω~(r)m = \widetilde{\Omega}(r), which we do using tools from Littlewood-Offord theory and estimates for binary Krawtchouk polynomials.Comment: 33 pages, to appear in Innovations in Theoretical Computer Science (ITCS 2022), v2: updated ref

    Transversal Problems In Sparse Graphs

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    Graph transversals are a classical branch of graph algorithms. In such a problem, one seeks a minimum-weight subset of nodes in a node-weighted graph GG which intersects all copies of subgraphs~FF from a fixed family F\mathcal F. In the first portion of this thesis we show two results related to even cycle transversal. %%Note rephrase this later. In Chapter \ref{ECTChapter}, we present our 47/7-approximation for even cycle transversal. To do this, we first apply a graph ``compression" method of Fiorini et al. % \cite{FioriniJP2010} which we describe in Chapter \ref{PreliminariesChapter}. For the analysis we repurpose the theory behind the 18/7-approximation for ``uncrossable" feedback vertex set problems of Berman and Yaroslavtsev %% \cite{BermanY2012} noting that we do not need the larger ``witness" cycles to be a cycle that we need to hit. This we do in Chapter \ref{BermanYaroChapter}. In Chapter \ref{ErdosPosaChapter} we present a simple proof of an Erdos Posa result, that for any natural number kk a planar graph GG either contains kk vertex disjoint even cycles, or a set XX of at most 9k9k such that G\XG \backslash X contains no even cycle. In the rest of this thesis, we show a result for dominating set. A dominating set SS in a graph is a set of vertices such that each node is in SS or adjacent to SS. In Chapter 6 we present a primal-dual (a+1)(a+1)-approximation for minimum weight dominating set in graphs of arboricity aa. At the end, we propose five open problems for future research

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum
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