124,613 research outputs found
A logic for n-dimensional hierarchical refinement
Hierarchical transition systems provide a popular mathematical structure to
represent state-based software applications in which different layers of
abstraction are represented by inter-related state machines. The decomposition
of high level states into inner sub-states, and of their transitions into inner
sub-transitions is common refinement procedure adopted in a number of
specification formalisms.
This paper introduces a hybrid modal logic for k-layered transition systems,
its first-order standard translation, a notion of bisimulation, and a modal
invariance result. Layered and hierarchical notions of refinement are also
discussed in this setting.Comment: In Proceedings Refine'15, arXiv:1606.0134
Finite Computational Structures and Implementations
What is computable with limited resources? How can we verify the correctness
of computations? How to measure computational power with precision? Despite the
immense scientific and engineering progress in computing, we still have only
partial answers to these questions. In order to make these problems more
precise, we describe an abstract algebraic definition of classical computation,
generalizing traditional models to semigroups. The mathematical abstraction
also allows the investigation of different computing paradigms (e.g. cellular
automata, reversible computing) in the same framework. Here we summarize the
main questions and recent results of the research of finite computation.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version
published by IEEE Computer Societ
Optimal Hierarchical Layouts for Cache-Oblivious Search Trees
This paper proposes a general framework for generating cache-oblivious
layouts for binary search trees. A cache-oblivious layout attempts to minimize
cache misses on any hierarchical memory, independent of the number of memory
levels and attributes at each level such as cache size, line size, and
replacement policy. Recursively partitioning a tree into contiguous subtrees
and prescribing an ordering amongst the subtrees, Hierarchical Layouts
generalize many commonly used layouts for trees such as in-order, pre-order and
breadth-first. They also generalize the various flavors of the van Emde Boas
layout, which have previously been used as cache-oblivious layouts.
Hierarchical Layouts thus unify all previous attempts at deriving layouts for
search trees.
The paper then derives a new locality measure (the Weighted Edge Product)
that mimics the probability of cache misses at multiple levels, and shows that
layouts that reduce this measure perform better. We analyze the various degrees
of freedom in the construction of Hierarchical Layouts, and investigate the
relative effect of each of these decisions in the construction of
cache-oblivious layouts. Optimizing the Weighted Edge Product for complete
binary search trees, we introduce the MinWEP layout, and show that it
outperforms previously used cache-oblivious layouts by almost 20%.Comment: Extended version with proofs added to the appendi
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Extending the Real-Time Maude Semantics of Ptolemy to Hierarchical DE Models
This paper extends our Real-Time Maude formalization of the semantics of flat
Ptolemy II discrete-event (DE) models to hierarchical models, including modal
models. This is a challenging task that requires combining synchronous
fixed-point computations with hierarchical structure. The synthesis of a
Real-Time Maude verification model from a Ptolemy II DE model, and the formal
verification of the synthesized model in Real-Time Maude, have been integrated
into Ptolemy II, enabling a model-engineering process that combines the
convenience of Ptolemy II DE modeling and simulation with formal verification
in Real-Time Maude.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
Random site dilution properties of frustrated magnets on a hierarchical lattice
We present a method to analyze magnetic properties of frustrated Ising spin
models on specific hierarchical lattices with random dilution. Disorder is
induced by dilution and geometrical frustration rather than randomness in the
internal couplings of the original Hamiltonian. The two-dimensional model
presented here possesses a macroscopic entropy at zero temperature in the large
size limit, very close to the Pauling estimate for spin-ice on pyrochlore
lattice, and a crossover towards a paramagnetic phase. The disorder due to
dilution is taken into account by considering a replicated version of the
recursion equations between partition functions at different lattice sizes. An
analysis at first order in replica number allows for a systematic
reorganization of the disorder configurations, leading to a recurrence scheme.
This method is numerically implemented to evaluate the thermodynamical
quantities such as specific heat and susceptibility in an external field.Comment: 26 pages, 11 figure
Continuity in cognition
Designing for continuous interaction requires
designers to consider the way in which human users can
perceive and evaluate an artefact’s observable behaviour,
in order to make inferences about its state and plan, and
execute their own continuous behaviour. Understanding
the human point of view in continuous interaction requires
an understanding of human causal reasoning, of
the way in which humans perceive and structure the
world, and of human cognition. We present a framework
for representing human cognition, and show briefly how it
relates to the analysis of structure in continuous interaction,
and the ways in which it may be applied in design
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