159,785 research outputs found
Nonisomorphic Ordered Sets with Arbitrarily Many Ranks That Produce Equal Decks
We prove that for any there is a pair of
nonisomorphic ordered sets such that and have equal maximal
and minimal decks, equal neighborhood decks, and there are ranks such that for each the decks obtained by removing the points
of rank are equal. The ranks do not contain
extremal elements and at each of the other ranks there are elements whose
removal will produce isomorphic cards. Moreover, we show that such sets can be
constructed such that only for ranks and , both without extremal
elements, the decks obtained by removing the points of rank are not
equal.Comment: 30 pages, 6 figures, straight LaTe
Partially ordered models
We provide a formal definition and study the basic properties of partially
ordered chains (POC). These systems were proposed to model textures in image
processing and to represent independence relations between random variables in
statistics (in the later case they are known as Bayesian networks). Our chains
are a generalization of probabilistic cellular automata (PCA) and their theory
has features intermediate between that of discrete-time processes and the
theory of statistical mechanical lattice fields. Its proper definition is based
on the notion of partially ordered specification (POS), in close analogy to the
theory of Gibbs measure. This paper contains two types of results. First, we
present the basic elements of the general theory of POCs: basic geometrical
issues, definition in terms of conditional probability kernels, extremal
decomposition, extremality and triviality, reconstruction starting from
single-site kernels, relations between POM and Gibbs fields. Second, we prove
three uniqueness criteria that correspond to the criteria known as bounded
uniformity, Dobrushin and disagreement percolation in the theory of Gibbs
measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat.
Phy
Superposition frames for adaptive time-frequency analysis and fast reconstruction
In this article we introduce a broad family of adaptive, linear
time-frequency representations termed superposition frames, and show that they
admit desirable fast overlap-add reconstruction properties akin to standard
short-time Fourier techniques. This approach stands in contrast to many
adaptive time-frequency representations in the extant literature, which, while
more flexible than standard fixed-resolution approaches, typically fail to
provide efficient reconstruction and often lack the regular structure necessary
for precise frame-theoretic analysis. Our main technical contributions come
through the development of properties which ensure that this construction
provides for a numerically stable, invertible signal representation. Our
primary algorithmic contributions come via the introduction and discussion of
specific signal adaptation criteria in deterministic and stochastic settings,
based respectively on time-frequency concentration and nonstationarity
detection. We conclude with a short speech enhancement example that serves to
highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio
A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging
Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging modalities such as hyper-spectral imaging, depth mapping, 3D profiling. However, the single-pixel technique requires sequential measurements resulting in a trade-off between spatial resolution and acquisition time, limiting real-time video applications to relatively low resolutions. Compressed sensing techniques can be used to improve this trade-off. However, in this low resolution regime, conventional compressed sensing techniques have limited impact due to lack of sparsity in the datasets. Here we present an alternative compressed sensing method in which we optimize the measurement order of the Hadamard basis, such that at discretized increments we obtain complete sampling for different spatial resolutions. In addition, this method uses deterministic acquisition, rather than the randomized sampling used in conventional compressed sensing. This so-called ‘Russian Dolls’ ordering also benefits from minimal computational overhead for image reconstruction. We find that this compressive approach performs as well as other compressive sensing techniques with greatly simplified post processing, resulting in significantly faster image reconstruction. Therefore, the proposed method may be useful for single-pixel imaging in the low resolution, high-frame rate regime, or video-rate acquisition
Accuracy of Sampling Quantum Phase Space in Photon Counting Experiment
We study the accuracy of determining the phase space quasidistribution of a
single quantized light mode by a photon counting experiment. We derive an exact
analytical formula for the error of the experimental outcome. This result
provides an estimation for the experimental parameters, such as the number of
events, required to determine the quasidistribution with assumed precision. Our
analysis also shows that it is in general not possible to compensate the
imperfectness of the photodetector in a numerical processing of the
experimental data. The discussion is illustrated with Monte Carlo simulations
of the photon counting experiment for the coherent state, the one photon Fock
state, and the Schroedinger cat state.Comment: 11 pages REVTeX, 5 figures, uses multicol, epsfig, and pstricks.
Submitted to Special Issue of Journal of Modern Optics on Quantum State
Preparation and Measuremen
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