1,023 research outputs found
A Logic for Non-Deterministic Parallel Abstract State Machines
We develop a logic which enables reasoning about single steps of
non-deterministic parallel Abstract State Machines (ASMs). Our logic builds
upon the unifying logic introduced by Nanchen and St\"ark for reasoning about
hierarchical (parallel) ASMs. Our main contribution to this regard is the
handling of non-determinism (both bounded and unbounded) within the logical
formalism. Moreover, we do this without sacrificing the completeness of the
logic for statements about single steps of non-deterministic parallel ASMs,
such as invariants of rules, consistency conditions for rules, or step-by-step
equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748
SiL: An Approach for Adjusting Applications to Heterogeneous Systems Under Perturbations
Scientific applications consist of large and computationally-intensive loops.
Dynamic loop scheduling (DLS) techniques are used to load balance the execution
of such applications. Load imbalance can be caused by variations in loop
iteration execution times due to problem, algorithmic, or systemic
characteristics (also, perturbations). The following question motivates this
work: "Given an application, a high-performance computing (HPC) system, and
both their characteristics and interplay, which DLS technique will achieve
improved performance under unpredictable perturbations?" Existing work only
considers perturbations caused by variations in the HPC system delivered
computational speeds. However, perturbations in available network bandwidth or
latency are inevitable on production HPC systems. Simulator in the loop (SiL)
is introduced, herein, as a new control-theoretic inspired approach to
dynamically select DLS techniques that improve the performance of applications
on heterogeneous HPC systems under perturbations. The present work examines the
performance of six applications on a heterogeneous system under all above
system perturbations. The SiL proof of concept is evaluated using simulation.
The performance results confirm the initial hypothesis that no single DLS
technique can deliver best performance in all scenarios, while the SiL-based
DLS selection delivered improved application performance in most experiments
On the structure of acyclic binary relations
We investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representation by means of incidence matrices. Acyclic binary relations can be extended to the asymmetric part of a linear order, so that, in particular, any directed acyclic graph has a topological sorting.This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P, ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain)
On the probabilistic min spanning tree Problem
We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively
A Computational Approach for Designing Tiger Corridors in India
Wildlife corridors are components of landscapes, which facilitate the
movement of organisms and processes between intact habitat areas, and thus
provide connectivity between the habitats within the landscapes. Corridors are
thus regions within a given landscape that connect fragmented habitat patches
within the landscape. The major concern of designing corridors as a
conservation strategy is primarily to counter, and to the extent possible,
mitigate the effects of habitat fragmentation and loss on the biodiversity of
the landscape, as well as support continuance of land use for essential local
and global economic activities in the region of reference. In this paper, we
use game theory, graph theory, membership functions and chain code algorithm to
model and design a set of wildlife corridors with tiger (Panthera tigris
tigris) as the focal species. We identify the parameters which would affect the
tiger population in a landscape complex and using the presence of these
identified parameters construct a graph using the habitat patches supporting
tiger presence in the landscape complex as vertices and the possible paths
between them as edges. The passage of tigers through the possible paths have
been modelled as an Assurance game, with tigers as an individual player. The
game is played recursively as the tiger passes through each grid considered for
the model. The iteration causes the tiger to choose the most suitable path
signifying the emergence of adaptability. As a formal explanation of the game,
we model this interaction of tiger with the parameters as deterministic finite
automata, whose transition function is obtained by the game payoff.Comment: 12 pages, 5 figures, 6 tables, NGCT conference 201
On a Convex Set with Nondifferentiable Metric Projection
A remarkable example of a nonempty closed convex set in the Euclidean plane
for which the directional derivative of the metric projection mapping fails to
exist was constructed by A. Shapiro. In this paper, we revisit and modify that
construction to obtain a convex set with smooth boundary which possesses the
same property
Can Genetic Programming Do Manifold Learning Too?
Exploratory data analysis is a fundamental aspect of knowledge discovery that
aims to find the main characteristics of a dataset. Dimensionality reduction,
such as manifold learning, is often used to reduce the number of features in a
dataset to a manageable level for human interpretation. Despite this, most
manifold learning techniques do not explain anything about the original
features nor the true characteristics of a dataset. In this paper, we propose a
genetic programming approach to manifold learning called GP-MaL which evolves
functional mappings from a high-dimensional space to a lower dimensional space
through the use of interpretable trees. We show that GP-MaL is competitive with
existing manifold learning algorithms, while producing models that can be
interpreted and re-used on unseen data. A number of promising future directions
of research are found in the process.Comment: 16 pages, accepted in EuroGP '1
An order-theoretic characterization of the Howard-Bachmann-hierarchy
In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π₁¹-comprehension
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