2,133 research outputs found
Radiation recoil from highly distorted black holes
We present results from numerical evolutions of single black holes distorted
by axisymmetric, but equatorially asymmetric, gravitational (Brill) waves. Net
radiated energies, apparent horizon embeddings, and recoil velocities are shown
for a range of Brill wave parameters, including both even and odd parity
distortions of Schwarzschild black holes. We find that a wave packet initially
concentrated on the black hole throat, a likely model also for highly
asymmetric stellar collapse and late stage binary mergers, can generate a
maximum recoil velocity of about 150 (23) km/sec for even (odd) parity
perturbations, significantly less than that required to eject black holes from
galactic cores.Comment: 15 pages, 8 figure
Time for dithering: fast and quantized random embeddings via the restricted isometry property
Recently, many works have focused on the characterization of non-linear
dimensionality reduction methods obtained by quantizing linear embeddings,
e.g., to reach fast processing time, efficient data compression procedures,
novel geometry-preserving embeddings or to estimate the information/bits stored
in this reduced data representation. In this work, we prove that many linear
maps known to respect the restricted isometry property (RIP) can induce a
quantized random embedding with controllable multiplicative and additive
distortions with respect to the pairwise distances of the data points beings
considered. In other words, linear matrices having fast matrix-vector
multiplication algorithms (e.g., based on partial Fourier ensembles or on the
adjacency matrix of unbalanced expanders) can be readily used in the definition
of fast quantized embeddings with small distortions. This implication is made
possible by applying right after the linear map an additive and random "dither"
that stabilizes the impact of the uniform scalar quantization operator applied
afterwards. For different categories of RIP matrices, i.e., for different
linear embeddings of a metric space
in with , we derive upper bounds on the
additive distortion induced by quantization, showing that it decays either when
the embedding dimension increases or when the distance of a pair of
embedded vectors in decreases. Finally, we develop a novel
"bi-dithered" quantization scheme, which allows for a reduced distortion that
decreases when the embedding dimension grows and independently of the
considered pair of vectors.Comment: Keywords: random projections, non-linear embeddings, quantization,
dither, restricted isometry property, dimensionality reduction, compressive
sensing, low-complexity signal models, fast and structured sensing matrices,
quantized rank-one projections (31 pages
Gravity-Inspired Graph Autoencoders for Directed Link Prediction
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged
as powerful node embedding methods. In particular, graph AE and VAE were
successfully leveraged to tackle the challenging link prediction problem,
aiming at figuring out whether some pairs of nodes from a graph are connected
by unobserved edges. However, these models focus on undirected graphs and
therefore ignore the potential direction of the link, which is limiting for
numerous real-life applications. In this paper, we extend the graph AE and VAE
frameworks to address link prediction in directed graphs. We present a new
gravity-inspired decoder scheme that can effectively reconstruct directed
graphs from a node embedding. We empirically evaluate our method on three
different directed link prediction tasks, for which standard graph AE and VAE
perform poorly. We achieve competitive results on three real-world graphs,
outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management
(CIKM 2019
The Power of Asymmetry in Binary Hashing
When approximating binary similarity using the hamming distance between short
binary hashes, we show that even if the similarity is symmetric, we can have
shorter and more accurate hashes by using two distinct code maps. I.e. by
approximating the similarity between and as the hamming distance
between and , for two distinct binary codes , rather than as
the hamming distance between and .Comment: Accepted to NIPS 2013, 9 pages, 5 figure
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