7,197 research outputs found

    Polynomial-time sortable stacks of burnt pancakes

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    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

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    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

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    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

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    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

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    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

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    It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose ff-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

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    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

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    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

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    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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