7,197 research outputs found
Polynomial-time sortable stacks of burnt pancakes
Pancake flipping, a famous open problem in computer science, can be
formalised as the problem of sorting a permutation of positive integers using
as few prefix reversals as possible. In that context, a prefix reversal of
length k reverses the order of the first k elements of the permutation. The
burnt variant of pancake flipping involves permutations of signed integers, and
reversals in that case not only reverse the order of elements but also invert
their signs. Although three decades have now passed since the first works on
these problems, neither their computational complexity nor the maximal number
of prefix reversals needed to sort a permutation is yet known. In this work, we
prove a new lower bound for sorting burnt pancakes, and show that an important
class of permutations, known as "simple permutations", can be optimally sorted
in polynomial time.Comment: Accepted pending minor revisio
On the complexity and the information content of cosmic structures
The emergence of cosmic structure is commonly considered one of the most
complex phenomena in Nature. However, this complexity has never been defined
nor measured in a quantitative and objective way. In this work we propose a
method to measure the information content of cosmic structure and to quantify
the complexity that emerges from it, based on Information Theory. The emergence
of complex evolutionary patterns is studied with a statistical symbolic
analysis of the datastream produced by state-of-the-art cosmological
simulations of forming galaxy clusters. This powerful approach allows us to
measure how many bits of information are necessary to predict the evolution of
energy fields in a statistical way, and it offers a simple way to quantify
when, where and how the cosmic gas behaves in complex ways. The most complex
behaviors are found in the peripheral regions of galaxy clusters, where
supersonic flows drive shocks and large energy fluctuations over a few tens of
million years. Describing the evolution of magnetic energy requires at least a
twice as large amount of bits than for the other energy fields. When radiative
cooling and feedback from galaxy formation are considered, the cosmic gas is
overall found to double its degree of complexity. In the future, Cosmic
Information Theory can significantly increase our understanding of the
emergence of cosmic structure as it represents an innovative framework to
design and analyze complex simulations of the Universe in a simple, yet
powerful way.Comment: 15 pages, 14 figures. MNRAS accepted, in pres
The Zeldovich approximation: key to understanding Cosmic Web complexity
We describe how the dynamics of cosmic structure formation defines the
intricate geometric structure of the spine of the cosmic web. The Zeldovich
approximation is used to model the backbone of the cosmic web in terms of its
singularity structure. The description by Arnold et al. (1982) in terms of
catastrophe theory forms the basis of our analysis.
This two-dimensional analysis involves a profound assessment of the
Lagrangian and Eulerian projections of the gravitationally evolving
four-dimensional phase-space manifold. It involves the identification of the
complete family of singularity classes, and the corresponding caustics that we
see emerging as structure in Eulerian space evolves. In particular, as it is
instrumental in outlining the spatial network of the cosmic web, we investigate
the nature of spatial connections between these singularities.
The major finding of our study is that all singularities are located on a set
of lines in Lagrangian space. All dynamical processes related to the caustics
are concentrated near these lines. We demonstrate and discuss extensively how
all 2D singularities are to be found on these lines. When mapping this spatial
pattern of lines to Eulerian space, we find a growing connectedness between
initially disjoint lines, resulting in a percolating network. In other words,
the lines form the blueprint for the global geometric evolution of the cosmic
web.Comment: 37 pages, 21 figures, accepted for publication in MNRA
Pancake Flipping is Hard
Pancake Flipping is the problem of sorting a stack of pancakes of different
sizes (that is, a permutation), when the only allowed operation is to insert a
spatula anywhere in the stack and to flip the pancakes above it (that is, to
perform a prefix reversal). In the burnt variant, one side of each pancake is
marked as burnt, and it is required to finish with all pancakes having the
burnt side down. Computing the optimal scenario for any stack of pancakes and
determining the worst-case stack for any stack size have been challenges over
more than three decades. Beyond being an intriguing combinatorial problem in
itself, it also yields applications, e.g. in parallel computing and
computational biology. In this paper, we show that the Pancake Flipping
problem, in its original (unburnt) variant, is NP-hard, thus answering the
long-standing question of its computational complexity.Comment: Corrected reference
Lifeworld Analysis
We argue that the analysis of agent/environment interactions should be
extended to include the conventions and invariants maintained by agents
throughout their activity. We refer to this thicker notion of environment as a
lifeworld and present a partial set of formal tools for describing structures
of lifeworlds and the ways in which they computationally simplify activity. As
one specific example, we apply the tools to the analysis of the Toast system
and show how versions of the system with very different control structures in
fact implement a common control structure together with different conventions
for encoding task state in the positions or states of objects in the
environment.Comment: See http://www.jair.org/ for any accompanying file
Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions
It is well-known that any admissible unidirectional heuristic search
algorithm must expand all states whose -value is smaller than the optimal
solution cost when using a consistent heuristic. Such states are called "surely
expanded" (s.e.). A recent study characterized s.e. pairs of states for
bidirectional search with consistent heuristics: if a pair of states is s.e.
then at least one of the two states must be expanded. This paper derives a
lower bound, VC, on the minimum number of expansions required to cover all s.e.
pairs, and present a new admissible front-to-end bidirectional heuristic search
algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no
more than 2VC expansions. We further prove that no admissible front-to-end
algorithm has a worst case better than 2VC. Experimental results show that NBS
competes with or outperforms existing bidirectional search algorithms, and
often outperforms A* as well.Comment: Accepted to IJCAI 2017. Camera ready version with new timing result
Hydrodynamic approach to the evolution of cosmological structures
A hydrodynamic formulation of the evolution of large-scale structure in the
Universe is presented. It relies on the spatially coarse-grained description of
the dynamical evolution of a many-body gravitating system. Because of the
assumed irrelevance of short-range (``collisional'') interactions, the way to
tackle the hydrodynamic equations is essentially different from the usual case.
The main assumption is that the influence of the small scales over the
large-scale evolution is weak: this idea is implemented in the form of a
large-scale expansion for the coarse-grained equations. This expansion builds a
framework in which to derive in a controlled manner the popular ``dust'' model
(as the lowest-order term) and the ``adhesion'' model (as the first-order
correction). It provides a clear physical interpretation of the assumptions
involved in these models and also the possibility to improve over them.Comment: 14 pages, 3 figures. Version to appear in Phys. Rev.
Review of industry-proposed in-pile thermionic space reactors. Volume I - General
Diode and reactor design and nuclear fuels including uranium carbide alloys, uranium dioxide and uranium dioxide cermets for industry proposed in-pile thermionic space reactor
On the efficiency of estimating penetrating rank on large graphs
P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute P-Rank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude
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