74,192 research outputs found
Quantitative Redundancy in Partial Implications
We survey the different properties of an intuitive notion of redundancy, as a
function of the precise semantics given to the notion of partial implication.
The final version of this survey will appear in the Proceedings of the Int.
Conf. Formal Concept Analysis, 2015.Comment: Int. Conf. Formal Concept Analysis, 201
Construct redundancy in process modelling grammars: Improving the explanatory power of ontological analysis
Conceptual modelling supports developers and users of information systems in areas of documentation, analysis or system redesign. The ongoing interest in the modelling of business processes has led to a variety of different grammars, raising the question of the quality of these grammars for modelling. An established way of evaluating the quality of a modelling grammar is by means of an ontological analysis, which can determine the extent to which grammars contain construct deficit, overload, excess or redundancy. While several studies have shown the relevance of most of these criteria, predictions about construct redundancy have yielded inconsistent results in the past, with some studies suggesting that redundancy may even be beneficial for modelling in practice. In this paper we seek to contribute to clarifying the concept of construct redundancy by introducing a revision to the ontological analysis method. Based on the concept of inheritance we propose an approach that distinguishes between specialized and distinct construct redundancy. We demonstrate the potential explanatory power of the revised method by reviewing and clarifying previous results found in the literature
Relative Entailment Among Probabilistic Implications
We study a natural variant of the implicational fragment of propositional
logic. Its formulas are pairs of conjunctions of positive literals, related
together by an implicational-like connective; the semantics of this sort of
implication is defined in terms of a threshold on a conditional probability of
the consequent, given the antecedent: we are dealing with what the data
analysis community calls confidence of partial implications or association
rules. Existing studies of redundancy among these partial implications have
characterized so far only entailment from one premise and entailment from two
premises, both in the stand-alone case and in the case of presence of
additional classical implications (this is what we call "relative entailment").
By exploiting a previously noted alternative view of the entailment in terms of
linear programming duality, we characterize exactly the cases of entailment
from arbitrary numbers of premises, again both in the stand-alone case and in
the case of presence of additional classical implications. As a result, we
obtain decision algorithms of better complexity; additionally, for each
potential case of entailment, we identify a critical confidence threshold and
show that it is, actually, intrinsic to each set of premises and antecedent of
the conclusion
A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments
As quantum information science approaches the goal of constructing quantum
computers, understanding loss of information through decoherence becomes
increasingly important. The information about a system that can be obtained
from its environment can facilitate quantum control and error correction.
Moreover, observers gain most of their information indirectly, by monitoring
(primarily photon) environments of the "objects of interest." Exactly how this
information is inscribed in the environment is essential for the emergence of
"the classical" from the quantum substrate. In this paper, we examine how
many-qubit (or many-spin) environments can store information about a single
system. The information lost to the environment can be stored redundantly, or
it can be encoded in entangled modes of the environment. We go on to show that
randomly chosen states of the environment almost always encode the information
so that an observer must capture a majority of the environment to deduce the
system's state. Conversely, in the states produced by a typical decoherence
process, information about a particular observable of the system is stored
redundantly. This selective proliferation of "the fittest information" (known
as Quantum Darwinism) plays a key role in choosing the preferred, effectively
classical observables of macroscopic systems. The developing appreciation that
the environment functions not just as a garbage dump, but as a communication
channel, is extending our understanding of the environment's role in the
quantum-classical transition beyond the traditional paradigm of decoherence.Comment: 21 pages, 6 figures, RevTex 4. Submitted to Foundations of Physics
(Asher Peres Festschrift
Measure Functions for Frames
This paper addresses the natural question: ``How should frames be compared?''
We answer this question by quantifying the overcompleteness of all frames with
the same index set. We introduce the concept of a frame measure function: a
function which maps each frame to a continuous function. The comparison of
these functions induces an equivalence and partial order that allows for a
meaningful comparison of frames indexed by the same set. We define the
ultrafilter measure function, an explicit frame measure function that we show
is contained both algebraically and topologically inside all frame measure
functions. We explore additional properties of frame measure functions, showing
that they are additive on a large class of supersets-- those that come from so
called non-expansive frames. We apply our results to the Gabor setting,
computing the frame measure function of Gabor frames and establishing a new
result about supersets of Gabor frames.Comment: 54 pages, 1 figure; fixed typos, reformatted reference
Sonification, Musification, and Synthesis of Absolute Program Music
Presented at the 22nd International Conference on Auditory Display (ICAD-2016)When understood as a communication system, a musical work can be interpreted as data existing within three domains. In this interpretation an absolute domain is interposed as a communication channel between two programatic domains that act respectively
as source and receiver. As a source, a programatic domain creates, evolves, organizes, and represents a musical work. When acting as a receiver it re-constitutes acoustic signals into unique auditory experience. The absolute domain transmits physical vibrations
ranging from the stochastic structures of noise to the periodic waveforms of organized sound. Analysis of acoustic signals suggest recognition as a musical work requires signal periodicity to exceed some minimum. A methodological framework that satisfies
recent definitions of sonification is outlined. This framework is proposed to extend to musification through incorporation of data features that represent more traditional elements of a musical work such as melody, harmony, and rhythm
Exploring networks with traceroute-like probes: theory and simulations
Mapping the Internet generally consists in sampling the network from a
limited set of sources by using traceroute-like probes. This methodology, akin
to the merging of different spanning trees to a set of destination, has been
argued to introduce uncontrolled sampling biases that might produce statistical
properties of the sampled graph which sharply differ from the original ones. In
this paper we explore these biases and provide a statistical analysis of their
origin. We derive an analytical approximation for the probability of edge and
vertex detection that exploits the role of the number of sources and targets
and allows us to relate the global topological properties of the underlying
network with the statistical accuracy of the sampled graph. In particular, we
find that the edge and vertex detection probability depends on the betweenness
centrality of each element. This allows us to show that shortest path routed
sampling provides a better characterization of underlying graphs with broad
distributions of connectivity. We complement the analytical discussion with a
throughout numerical investigation of simulated mapping strategies in network
models with different topologies. We show that sampled graphs provide a fair
qualitative characterization of the statistical properties of the original
networks in a fair range of different strategies and exploration parameters.
Moreover, we characterize the level of redundancy and completeness of the
exploration process as a function of the topological properties of the network.
Finally, we study numerically how the fraction of vertices and edges discovered
in the sampled graph depends on the particular deployements of probing sources.
The results might hint the steps toward more efficient mapping strategies.Comment: This paper is related to cond-mat/0406404, with explorations of
different networks and complementary discussion
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