300 research outputs found
The “Public” in “Public Peace Process” and in “Mini-Publics:” A Dialogue between Democratic Theory and Peace Studies
The recent attention of peace studies scholars to the role of the public parallels an increased interest of democratic theorists in the legitimacy of mini-publics: initiatives that bring small groups of citizens together to discuss policy issues. In fact, democratic activists and peace activists who seek to engage the public face similar theoretical and practical challenges. The purpose of this article is to contribute to an emerging dialogue between the disciplines of democratic theory and peace studies. Such a dialogue can be beneficial in at least two ways: it allows an exploration of the role of legitimacy in public peace processes and the burdens that legitimacy put on the institutional design of such processes, and it allows an exploration of more ambitious models of public participation in the peace process
Approximately Counting Triangles in Sublinear Time
We consider the problem of estimating the number of triangles in a graph.
This problem has been extensively studied in both theory and practice, but all
existing algorithms read the entire graph. In this work we design a {\em
sublinear-time\/} algorithm for approximating the number of triangles in a
graph, where the algorithm is given query access to the graph. The allowed
queries are degree queries, vertex-pair queries and neighbor queries.
We show that for any given approximation parameter , the
algorithm provides an estimate such that with high constant
probability, , where
is the number of triangles in the graph . The expected query complexity of
the algorithm is , where
is the number of vertices in the graph and is the number of edges, and
the expected running time is . We also prove
that queries are necessary, thus establishing that
the query complexity of this algorithm is optimal up to polylogarithmic factors
in (and the dependence on ).Comment: To appear in the 56th Annual IEEE Symposium on Foundations of
Computer Science (FOCS 2015
Hard Properties with (Very) Short PCPPs and Their Applications
We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed ?, we construct a property P^(?)? {0,1}^n satisfying the following: Any testing algorithm for P^(?) requires ?(n) many queries, and yet P^(?) has a constant query PCPP whose proof size is O(n?log^(?)n), where log^(?) denotes the ? times iterated log function (e.g., log^(2)n = log log n). The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n?polylog(n)).
As an immediate application, we obtain stronger separations between the standard testing model and both the tolerant testing model and the erasure-resilient testing model: for every fixed ?, we construct a property that has a constant-query tester, but requires ?(n/log^(?)(n)) queries for every tolerant or erasure-resilient tester
On Partial Shape Correspondence and Functional Maps
While dealing with matching shapes to their parts, we often utilize an
instrument known as functional maps. The idea is to translate the shape
matching problem into ``convenient'' spaces by which matching is performed
algebraically by solving a least squares problem. Here, we argue that such
formulations, though popular in this field, introduce errors in the estimated
match when partiality is invoked. Such errors are unavoidable even when
considering advanced feature extraction networks, and they can be shown to
escalate with increasing degrees of shape partiality, adversely affecting the
learning capability of such systems. To circumvent these limitations, we
propose a novel approach for partial shape matching.
Our study of functional maps led us to a novel method that establishes direct
correspondence between partial and full shapes through feature matching
bypassing the need for functional map intermediate spaces. The Gromov distance
between metric spaces leads to the construction of the first part of our loss
functions. For regularization we use two options: a term based on the area
preserving property of the mapping, and a relaxed version of it without the
need to compute a functional map.
The proposed approach shows superior performance on the SHREC'16 dataset,
outperforming existing unsupervised methods for partial shape matching. In
particular, it achieves state-of-the-art result on the SHREC'16 HOLES
benchmark, superior also compared to supervised methods
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
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