195 research outputs found
Time-dependent iteration of random functions
Abstract In studying the iteration of random functions, the usual situation is to assume time-homogeneity of the process and some average contractivity condition. In this paper we change both of these conditions by investigating the iteration of time-dependent random functions where all the functions converge (as the iterations proceed) uniformly to the identity. The behaviour of the iterates is remarkably different from the standard contractive situation. In particular, we show that for affine maps in R d the "chaos game" trajectory converges almost surely. This is in stark contrast to the usual situation where the trajectory moves ergodically throughout the attractor
A Compact Representation of Histopathology Images using Digital Stain Separation & Frequency-Based Encoded Local Projections
In recent years, histopathology images have been increasingly used as a
diagnostic tool in the medical field. The process of accurately diagnosing a
biopsy sample requires significant expertise in the field, and as such can be
time-consuming and is prone to uncertainty and error. With the advent of
digital pathology, using image recognition systems to highlight problem areas
or locate similar images can aid pathologists in making quick and accurate
diagnoses. In this paper, we specifically consider the encoded local
projections (ELP) algorithm, which has previously shown some success as a tool
for classification and recognition of histopathology images. We build on the
success of the ELP algorithm as a means for image classification and
recognition by proposing a modified algorithm which captures the local
frequency information of the image. The proposed algorithm estimates local
frequencies by quantifying the changes in multiple projections in local windows
of greyscale images. By doing so we remove the need to store the full
projections, thus significantly reducing the histogram size, and decreasing
computation time for image retrieval and classification tasks. Furthermore, we
investigate the effectiveness of applying our method to histopathology images
which have been digitally separated into their hematoxylin and eosin stain
components. The proposed algorithm is tested on the publicly available invasive
ductal carcinoma (IDC) data set. The histograms are used to train an SVM to
classify the data. The experiments showed that the proposed method outperforms
the original ELP algorithm in image retrieval tasks. On classification tasks,
the results are found to be comparable to state-of-the-art deep learning
methods and better than many handcrafted features from the literature.Comment: Accepted for publication in the International Conference on Image
Analysis and Recognition (ICIAR 2019
Self-similar measures in multi-sector endogenous growth models
We analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Uzawa–Lucas (1965, 1988) model and an extended three-sector version as in La Torre and Marsiglio (2010). As in the case of sustained growth the optimal dynamics of the state variables are not stationary, we focus on the dynamics of the capital ratio variables, and we show that, through appropriate log-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some (possibly fractal) compact set. This proves that also the steady state of endogenous growth models—i.e., the stochastic balanced growth path equilibrium—might have a fractal nature. We also provide some sufficient conditions under which the associated self-similar measures turn out to be either singular or absolutely continuous (for the three-sector model we only consider the singularity)
Self-Similar Measures in Multi-Sector Endogenous Growth Models
We analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Uzawa-Lucas (1965, 1988) model and an extended three-sector version as in La Torre and Marsiglio (2010). As in the case of sustained growth the optimal dynamics of the state variables are not stationary, we focus on the dynamics of the capital ratio variables, and we show that, through appropriate log-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some (possibly fractal) compact set. This proves that also the steady state of endogenous growth models-i.e., the stochastic balanced growth path equilibrium-might have a fractal nature. We also provide some sufficient conditions under which the associated self-similar measures turn out to be either singular or absolutely continuous (for the three-sector model we only consider the singularity)
Generalized Fractal Transforms with Condensation: a Macroeconomic-Epidemiological Application
Public Debt Dynamics under Ambiguity by Means of Iterated Function Systems on Density Functions
THE MONGE-KANTOROVICH METRIC ON MULTIMEASURES AND SELF-SIMILAR MULTIMEASURES
Abstract. For a metric space (X, d) the classical Monge-Kantorovich metric d M gives a distance between two probability measures on X which is tied to the underlying distance d on X in an essential way. In this paper, we extend the Monge-Kantorovich metric to signed measures and set-valued measures (multimeasures) and, in each case, prove completeness of a suitable space of these measures. Using this extension as a framework, we construct self-similar multimeasures by using an IFS-type Markov operator
Iterated function systems with place-dependent probabilities and the inverse problem of measure approximation using moments
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