1,487 research outputs found
Optimal Ramp Schemes and Related Combinatorial Objects
In 1996, Jackson and Martin proved that a strong ideal ramp scheme is
equivalent to an orthogonal array. However, there was no good characterization
of ideal ramp schemes that are not strong. Here we show the equivalence of
ideal ramp schemes to a new variant of orthogonal arrays that we term augmented
orthogonal arrays. We give some constructions for these new kinds of arrays,
and, as a consequence, we also provide parameter situations where ideal ramp
schemes exist but strong ideal ramp schemes do not exist
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance
A Polyhedral Study of Mixed 0-1 Set
We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set
Multi-Objective Optimization and Network Routing with Near-Term Quantum Computers
Multi-objective optimization is a ubiquitous problem that arises naturally in
many scientific and industrial areas. Network routing optimization with
multi-objective performance demands falls into this problem class, and finding
good quality solutions at large scales is generally challenging. In this work,
we develop a scheme with which near-term quantum computers can be applied to
solve multi-objective combinatorial optimization problems. We study the
application of this scheme to the network routing problem in detail, by first
mapping it to the multi-objective shortest path problem. Focusing on an
implementation based on the quantum approximate optimization algorithm (QAOA)
-- the go-to approach for tackling optimization problems on near-term quantum
computers -- we examine the Pareto plot that results from the scheme, and
qualitatively analyze its ability to produce Pareto-optimal solutions. We
further provide theoretical and numerical scaling analyses of the resource
requirements and performance of QAOA, and identify key challenges associated
with this approach. Finally, through Amazon Braket we execute small-scale
implementations of our scheme on the IonQ Harmony 11-qubit quantum computer
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Planning in constraint space for multi-body manipulation tasks
Robots are inherently limited by physical constraints on their link lengths, motor torques, battery
power and structural rigidity. To thrive in circumstances that push these limits, such as in search
and rescue scenarios, intelligent agents can use the available objects in their environment as
tools. Reasoning about arbitrary objects and how they can be placed together to create useful
structures such as ramps, bridges or simple machines is critical to push beyond one's physical
limitations. Unfortunately, the solution space is combinatorial in the number of available objects
and the configuration space of the chosen objects and the robot that uses the structure is high
dimensional.
To address these challenges, we propose using constraint satisfaction as a means to test the
feasibility of candidate structures and adopt search algorithms in the classical planning literature
to find sufficient designs. The key idea is that the interactions between the components of a
structure can be encoded as equality and inequality constraints on the configuration spaces of the
respective objects. Furthermore, constraints that are induced by a broadly defined action, such as
placing an object on another, can be grouped together using logical representations such as Planning
Domain Definition Language (PDDL). Then, a classical planning search algorithm can reason about
which set of constraints to impose on the available objects, iteratively creating a structure that
satisfies the task goals and the robot constraints. To demonstrate the effectiveness of this
framework, we present both simulation and real robot results with static structures such as ramps,
bridges and stairs, and quasi-static structures such as lever-fulcrum simple machines.Ph.D
Biomimetic Design for Efficient Robotic Performance in Dynamic Aquatic Environments - Survey
This manuscript is a review over the published articles on edge detection. At first, it provides theoretical background, and then reviews wide range of methods of edge detection in different categorizes. The review also studies the relationship between categories, and presents evaluations regarding to their application, performance, and implementation. It was stated that the edge detection methods structurally are a combination of image smoothing and image differentiation plus a post-processing for edge labelling. The image smoothing involves filters that reduce the noise, regularize the numerical computation, and provide a parametric representation of the image that works as a mathematical microscope to analyze it in different scales and increase the accuracy and reliability of edge detection. The image differentiation provides information of intensity transition in the image that is necessary to represent the position and strength of the edges and their orientation. The edge labelling calls for post-processing to suppress the false edges, link the dispread ones, and produce a uniform contour of objects
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