4,325 research outputs found
ON COUNTING SEQUENCES AND SOME RESEARCH QUESTIONS
A counting sequence is a list of all binary words of the same length. Counting sequences of any fixed odd Hamming distance between successive words (codewords) are discussed. Gray codes are examples of counting sequences having a single-bit change between neighboring codewords. We describe some results on Gray codes and highlight some research questions. The spectrum of bit changes or transition counts for individual variables for some uniform counting sequences is considered. We show some recent minor findings and pose remaining open questions
Rainbow Perfect Domination in Lattice Graphs
Let 0<n\in\mathbb{Z}. In the unit distance graph of , a perfect dominating set is understood as having induced components not necessarily trivial. A modification of that is proposed: a rainbow perfect dominating set, or RPDS, imitates a perfect-distance dominating set via a truncated metric; this has a distance involving at most once each coordinate direction taken as an edge color. Then, lattice-like RPDS s are built with their induced components C having: {i} vertex sets V(C) whose convex hulls are n-parallelotopes (resp., both (n-1)- and 0-cubes) and {ii} each V(C) contained in a corresponding rainbow sphere centered at C with radius n (resp., radii 1 and n-2)
Structure Learning of Partitioned Markov Networks
We learn the structure of a Markov Network between two groups of random
variables from joint observations. Since modelling and learning the full MN
structure may be hard, learning the links between two groups directly may be a
preferable option. We introduce a novel concept called the \emph{partitioned
ratio} whose factorization directly associates with the Markovian properties of
random variables across two groups. A simple one-shot convex optimization
procedure is proposed for learning the \emph{sparse} factorizations of the
partitioned ratio and it is theoretically guaranteed to recover the correct
inter-group structure under mild conditions. The performance of the proposed
method is experimentally compared with the state of the art MN structure
learning methods using ROC curves. Real applications on analyzing
bipartisanship in US congress and pairwise DNA/time-series alignments are also
reported.Comment: Camera Ready for ICML 2016. Fixed some minor typo
Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted Identifying Code, (Open) Open Locating-Dominating Set and Metric Dimension) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP-complete, even for interval graphs of diameter 2 and permutation graphs of diameter 2. While Identifying Code and (Open) Locating-Dominating Set are trivially fixed-parameter-tractable when parameterized by solution size, it is known that in the same setting Metric Dimension is W[2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
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