34,774 research outputs found
Connected component identification and cluster update on GPU
Cluster identification tasks occur in a multitude of contexts in physics and
engineering such as, for instance, cluster algorithms for simulating spin
models, percolation simulations, segmentation problems in image processing, or
network analysis. While it has been shown that graphics processing units (GPUs)
can result in speedups of two to three orders of magnitude as compared to
serial codes on CPUs for the case of local and thus naturally parallelized
problems such as single-spin flip update simulations of spin models, the
situation is considerably more complicated for the non-local problem of cluster
or connected component identification. I discuss the suitability of different
approaches of parallelization of cluster labeling and cluster update algorithms
for calculations on GPU and compare to the performance of serial
implementations.Comment: 15 pages, 14 figures, one table, submitted to PR
Exact Meander Asymptotics: a Numerical Check
This note addresses the meander enumeration problem: "Count all topologically
inequivalent configurations of a closed planar non self-intersecting curve
crossing a line through a given number of points". We review a description of
meanders introduced recently in terms of the coupling to gravity of a
two-flavored fully-packed loop model. The subsequent analytic predictions for
various meandric configuration exponents are checked against exact enumeration,
using a transfer matrix method, with an excellent agreement.Comment: 48 pages, 24 figures, tex, harvmac, eps
An attentive neural architecture for joint segmentation and parsing and its application to real estate ads
In processing human produced text using natural language processing (NLP)
techniques, two fundamental subtasks that arise are (i) segmentation of the
plain text into meaningful subunits (e.g., entities), and (ii) dependency
parsing, to establish relations between subunits. In this paper, we develop a
relatively simple and effective neural joint model that performs both
segmentation and dependency parsing together, instead of one after the other as
in most state-of-the-art works. We will focus in particular on the real estate
ad setting, aiming to convert an ad to a structured description, which we name
property tree, comprising the tasks of (1) identifying important entities of a
property (e.g., rooms) from classifieds and (2) structuring them into a tree
format. In this work, we propose a new joint model that is able to tackle the
two tasks simultaneously and construct the property tree by (i) avoiding the
error propagation that would arise from the subtasks one after the other in a
pipelined fashion, and (ii) exploiting the interactions between the subtasks.
For this purpose, we perform an extensive comparative study of the pipeline
methods and the new proposed joint model, reporting an improvement of over
three percentage points in the overall edge F1 score of the property tree.
Also, we propose attention methods, to encourage our model to focus on salient
tokens during the construction of the property tree. Thus we experimentally
demonstrate the usefulness of attentive neural architectures for the proposed
joint model, showcasing a further improvement of two percentage points in edge
F1 score for our application.Comment: Preprint - Accepted for publication in Expert Systems with
Application
1-Safe Petri nets and special cube complexes: equivalence and applications
Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net
unfolds into an event structure . By a result of Thiagarajan
(1996 and 2002), these unfoldings are exactly the trace regular event
structures. Thiagarajan (1996 and 2002) conjectured that regular event
structures correspond exactly to trace regular event structures. In a recent
paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on
the striking bijection between domains of event structures, median graphs, and
CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we
proved that Thiagarajan's conjecture is true for regular event structures whose
domains are principal filters of universal covers of (virtually) finite special
cube complexes.
In the current paper, we prove the converse: to any finite 1-safe Petri net
one can associate a finite special cube complex such that the
domain of the event structure (obtained as the unfolding of
) is a principal filter of the universal cover of .
This establishes a bijection between 1-safe Petri nets and finite special cube
complexes and provides a combinatorial characterization of trace regular event
structures.
Using this bijection and techniques from graph theory and geometry (MSO
theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet
another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that
the monadic second order logic of a 1-safe Petri net is decidable if and only
if its unfolding is grid-free.
Our counterexample is the trace regular event structure
which arises from a virtually special square complex . The domain of
is grid-free (because it is hyperbolic), but the MSO
theory of the event structure is undecidable
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