5,431 research outputs found
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems
We develop an inexact primal-dual first-order smoothing framework to solve a
class of non-bilinear saddle point problems with primal strong convexity.
Compared with existing methods, our framework yields a significant improvement
over the primal oracle complexity, while it has competitive dual oracle
complexity. In addition, we consider the situation where the primal-dual
coupling term has a large number of component functions. To efficiently handle
this situation, we develop a randomized version of our smoothing framework,
which allows the primal and dual sub-problems in each iteration to be solved by
randomized algorithms inexactly in expectation. The convergence of this
framework is analyzed both in expectation and with high probability. In terms
of the primal and dual oracle complexities, this framework significantly
improves over its deterministic counterpart. As an important application, we
adapt both frameworks for solving convex optimization problems with many
functional constraints. To obtain an -optimal and
-feasible solution, both frameworks achieve the best-known oracle
complexities (in terms of their dependence on )
SLIC Based Digital Image Enlargement
Low resolution image enhancement is a classical computer vision problem.
Selecting the best method to reconstruct an image to a higher resolution with
the limited data available in the low-resolution image is quite a challenge. A
major drawback from the existing enlargement techniques is the introduction of
color bleeding while interpolating pixels over the edges that separate distinct
colors in an image. The color bleeding causes to accentuate the edges with new
colors as a result of blending multiple colors over adjacent regions. This
paper proposes a novel approach to mitigate the color bleeding by segmenting
the homogeneous color regions of the image using Simple Linear Iterative
Clustering (SLIC) and applying a higher order interpolation technique
separately on the isolated segments. The interpolation at the boundaries of
each of the isolated segments is handled by using a morphological operation.
The approach is evaluated by comparing against several frequently used image
enlargement methods such as bilinear and bicubic interpolation by means of Peak
Signal-to-Noise-Ratio (PSNR) value. The results obtained exhibit that the
proposed method outperforms the baseline methods by means of PSNR and also
mitigates the color bleeding at the edges which improves the overall
appearance.Comment: 6 page
Deterministic parallel algorithms for bilinear objective functions
Many randomized algorithms can be derandomized efficiently using either the
method of conditional expectations or probability spaces with low independence.
A series of papers, beginning with work by Luby (1988), showed that in many
cases these techniques can be combined to give deterministic parallel (NC)
algorithms for a variety of combinatorial optimization problems, with low time-
and processor-complexity.
We extend and generalize a technique of Luby for efficiently handling
bilinear objective functions. One noteworthy application is an NC algorithm for
maximal independent set. On a graph with edges and vertices, this
takes time and processors, nearly
matching the best randomized parallel algorithms. Other applications include
reduced processor counts for algorithms of Berger (1997) for maximum acyclic
subgraph and Gale-Berlekamp switching games.
This bilinear factorization also gives better algorithms for problems
involving discrepancy. An important application of this is to automata-fooling
probability spaces, which are the basis of a notable derandomization technique
of Sivakumar (2002). Our method leads to large reduction in processor
complexity for a number of derandomization algorithms based on
automata-fooling, including set discrepancy and the Johnson-Lindenstrauss
Lemma
Introduction to the nonequilibrium functional renormalization group
In these lectures we introduce the functional renormalization group out of
equilibrium. While in thermal equilibrium typically a Euclidean formulation is
adequate, nonequilibrium properties require real-time descriptions. For quantum
systems specified by a given density matrix at initial time, a generating
functional for real-time correlation functions can be written down using the
Schwinger-Keldysh closed time path. This can be used to construct a
nonequilibrium functional renormalization group along similar lines as for
Euclidean field theories in thermal equilibrium. Important differences include
the absence of a fluctuation-dissipation relation for general
out-of-equilibrium situations. The nonequilibrium renormalization group takes
on a particularly simple form at a fixed point, where the corresponding
scale-invariant system becomes independent of the details of the initial
density matrix. We discuss some basic examples, for which we derive a hierarchy
of fixed point solutions with increasing complexity from vacuum and thermal
equilibrium to nonequilibrium. The latter solutions are then associated to the
phenomenon of turbulence in quantum field theory.Comment: Lectures given at the 49th Schladming Winter School `Physics at all
scales: The Renormalization Group' (to appear in the proceedings); 24 pages,
3 figure
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