17,187 research outputs found
A Logic of Reachable Patterns in Linked Data-Structures
We define a new decidable logic for expressing and checking invariants of
programs that manipulate dynamically-allocated objects via pointers and
destructive pointer updates. The main feature of this logic is the ability to
limit the neighborhood of a node that is reachable via a regular expression
from a designated node. The logic is closed under boolean operations
(entailment, negation) and has a finite model property. The key technical
result is the proof of decidability. We show how to express precondition,
postconditions, and loop invariants for some interesting programs. It is also
possible to express properties such as disjointness of data-structures, and
low-level heap mutations. Moreover, our logic can express properties of
arbitrary data-structures and of an arbitrary number of pointer fields. The
latter provides a way to naturally specify postconditions that relate the
fields on entry to a procedure to the fields on exit. Therefore, it is possible
to use the logic to automatically prove partial correctness of programs
performing low-level heap mutations
Simple Local Computation Algorithms for the General Lovasz Local Lemma
We consider the task of designing Local Computation Algorithms (LCA) for
applications of the Lov\'{a}sz Local Lemma (LLL). LCA is a class of sublinear
algorithms proposed by Rubinfeld et al.~\cite{Ronitt} that have received a lot
of attention in recent years. The LLL is an existential, sufficient condition
for a collection of sets to have non-empty intersection (in applications,
often, each set comprises all objects having a certain property). The
ground-breaking algorithm of Moser and Tardos~\cite{MT} made the LLL fully
constructive, following earlier results by Beck~\cite{beck_lll} and
Alon~\cite{alon_lll} giving algorithms under significantly stronger LLL-like
conditions. LCAs under those stronger conditions were given in~\cite{Ronitt},
where it was asked if the Moser-Tardos algorithm can be used to design LCAs
under the standard LLL condition. The main contribution of this paper is to
answer this question affirmatively. In fact, our techniques yield LCAs for
settings beyond the standard LLL condition
Tverberg plus constraints
Many of the strengthenings and extensions of the topological Tverberg theorem
can be derived with surprising ease directly from the original theorem: For
this we introduce a proof technique that combines a concept of "Tverberg
unavoidable subcomplexes" with the observation that Tverberg points that
equalize the distance from such a subcomplex can be obtained from maps to an
extended target space.
Thus we obtain simple proofs for many variants of the topological Tverberg
theorem, such as the colored Tverberg theorem of Zivaljevic and Vrecica (1992).
We also get a new strengthened version of the generalized van Kampen-Flores
theorem by Sarkaria (1991) and Volovikov (1996), an affine version of their
"j-wise disjoint" Tverberg theorem, and a topological version of Soberon's
(2013) result on Tverberg points with equal barycentric coordinates.Comment: 15 pages; revised version, accepted for publication in Bulletin
London Math. Societ
Finitely dependent coloring
We prove that proper coloring distinguishes between block-factors and
finitely dependent stationary processes. A stochastic process is finitely
dependent if variables at sufficiently well-separated locations are
independent; it is a block-factor if it can be expressed as an equivariant
finite-range function of independent variables. The problem of finding
non-block-factor finitely dependent processes dates back to 1965. The first
published example appeared in 1993, and we provide arguably the first natural
examples. More precisely, Schramm proved in 2008 that no stationary 1-dependent
3-coloring of the integers exists, and conjectured that no stationary
k-dependent q-coloring exists for any k and q. We disprove this by constructing
a 1-dependent 4-coloring and a 2-dependent 3-coloring, thus resolving the
question for all k and q.
Our construction is canonical and natural, yet very different from all
previous schemes. In its pure form it yields precisely the two finitely
dependent colorings mentioned above, and no others. The processes provide
unexpected connections between extremal cases of the Lovasz local lemma and
descent and peak sets of random permutations. Neither coloring can be expressed
as a block-factor, nor as a function of a finite-state Markov chain; indeed, no
stationary finitely dependent coloring can be so expressed. We deduce
extensions involving d dimensions and shifts of finite type; in fact, any
non-degenerate shift of finite type also distinguishes between block-factors
and finitely dependent processes
Laplacian-Steered Neural Style Transfer
Neural Style Transfer based on Convolutional Neural Networks (CNN) aims to
synthesize a new image that retains the high-level structure of a content
image, rendered in the low-level texture of a style image. This is achieved by
constraining the new image to have high-level CNN features similar to the
content image, and lower-level CNN features similar to the style image. However
in the traditional optimization objective, low-level features of the content
image are absent, and the low-level features of the style image dominate the
low-level detail structures of the new image. Hence in the synthesized image,
many details of the content image are lost, and a lot of inconsistent and
unpleasing artifacts appear. As a remedy, we propose to steer image synthesis
with a novel loss function: the Laplacian loss. The Laplacian matrix
("Laplacian" in short), produced by a Laplacian operator, is widely used in
computer vision to detect edges and contours. The Laplacian loss measures the
difference of the Laplacians, and correspondingly the difference of the detail
structures, between the content image and a new image. It is flexible and
compatible with the traditional style transfer constraints. By incorporating
the Laplacian loss, we obtain a new optimization objective for neural style
transfer named Lapstyle. Minimizing this objective will produce a stylized
image that better preserves the detail structures of the content image and
eliminates the artifacts. Experiments show that Lapstyle produces more
appealing stylized images with less artifacts, without compromising their
"stylishness".Comment: Accepted by the ACM Multimedia Conference (MM) 2017. 9 pages, 65
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