Local Entropy Measures Research Articles

Random expansion method for the generation of complex cellular automata

The complex behaviors in cellular automata have been widely developed in recent years to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. This type of automata has been frequently found either by conducting an exhaustive search or through a meticulous construction of the evolution rule. In this study, the specification of cellular automata with complex behaviors was obtained by utilizing randomly generated specimens. In particular, it was proposed that a cellular automaton of n states should be specified at random and then extended to another automaton with a higher number of states so that the original automaton operates as a periodic background where the additional states serve to define the gliders. Moreover, this study presents an explanation of this method. Furthermore, the random way of defining complex cellular automata was studied by using mean-field approximations for various states and local entropy measures. This specification was refined with a genetic algorithm to obtain specimens of a higher degree of complexity. By adopting this methodology, it was possible to generate complex automata with hundreds of states, demonstrating the fact that randomly defined local interactions with multiple states can construct complexity.

A novel approach to extracting useful information from noisy TFDs using 2D local entropy measures

The paper proposes a novel approach for extraction of useful information and blind source separation of signal components from noisy data in the time-frequency domain. The method is based on the local Rényi entropy calculated inside adaptive, data-driven 2D regions, the sizes of which are calculated utilizing the improved, relative intersection of confidence intervals (RICI) algorithm. One of the advantages of the proposed technique is that it does not require any prior knowledge on the signal, its components, or noise, but rather the processing is performed on the noisy signal mixtures. Also, it is shown that the method is robust to the selection of time-frequency distributions (TFDs). It has been tested for different signal-to-noise-ratios (SNRs), both for synthetic and real-life data. When compared to fixed TFD thresholding, adaptive TFD thresholding based on RICI rule and the 1D entropy-based approach, the proposed adaptive method significantly increases classification accuracy (by up to 11.53%) and F1 score (by up to 7.91%). Hence, this adaptive, data-driven, entropy-based technique is an efficient tool for extracting useful information from noisy data in the time-frequency domain.

Infrared small-target detection using multiscale gray difference weighted image entropy

We propose an effective small-target detection approach based on weighted image entropy. The approach weights the local entropy measure by the multiscale grayscale difference followed by an adaptive threshold operation, which aims to improve the signal-to-noise ratio for cases in which jamming objects in the scene have similar thermal intensity measure with respect to the background as small target. The detection capability of the proposed approach has been validated on six real sequences, and the results demonstrate its significance and improvement.

Local entropy as a measure for sampling solutions in constraint satisfaction problems

We introduce a novel entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random constraint satisfaction problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the space of solutions of the binary perceptron learning problem (a prototypical CSP), contains regions of very high-density of solutions. Despite being sub-dominant, these regions can be found by optimizing a local entropy measure. Building on these results, we construct a fast solver that relies exclusively on a local entropy estimate, and can be applied to general CSPs. We describe its performance not only for the perceptron learning problem but also for the random K-satisfiabilty problem (another prototypical CSP with a radically different structure), and show numerically that a simple zero-temperature Metropolis search in the smooth local entropy landscape can reach sub-dominant clusters of optimal solutions in a small number of steps, while standard Simulated Annealing either requires extremely long cooling procedures or just fails. We also discuss how the EdMC can heuristically be made even more efficient for the cases we studied.

Rényi Entropy Filter for Anomaly Detection With Eddy Current Remote Field Sensors

We consider a multichannel remote field eddy current sensor apparatus, which is installed on a mobile robot deployed in pipelines with the mission of detecting defects. Features in raw sensory data that are associated with defects could be masked by noise and therefore difficult to identify in some instances. In order to enhance these features that potentially identify defects, we propose an entropy filter that maps raw sensory data points into a local entropy measure. In the entropy space, data are then classified by means of a thresholding procedure based on the Neyman–Pearson criterion. The effectiveness of the algorithm is demonstrated by applying it to different data sets obtained from field trials.

Constrained Network Modularity

Static representations of protein interactions networks or PIN reflect measurements referred to a variety of conditions, including time. To partially bypass such limitation, gene expression information is usually integrated in the network to measure its “activity level.” In general, the entire PIN modular organization (complexes, pathways) can reveal changes of configuration whose functional significance depends on biological annotation. However, since network dynamics are based on the presence of different conditions leading to comparisons between normal and disease states, or between networks observed sequentially in time, our working hypothesis refers to the analysis of differential networks based on varying modularity and uncertainty. Two popular methods were applied and evaluated, k-core and Q-modularity, over a reference yeast dataset comprising a PIN of literature-curated data obtained from the fusion of heterogeneous measurements sources. While the functional aspect of interest is cell cycle and the corresponding interactions were isolated, the PIN dynamics were externally induced by time-course measured gene expression values, which we consider one of the “modularity drivers.” Notably, due to the nature of such expression values referred to the “just-in-time method,” we could specialize our approach according to three constrained modular configurations then comparatively assessed through local entropy measures.

Assessing software structure by entropy and information density

In this paper we show how the long range correlation and the local entropy measures in the software program can give indication about its structure. First we define a long range correlation and local entropy introducing a list of examples of use of those measures across different fields. We then present a method to calculate the long range correlation in the Software Engineering and we use that method in a Case Study. Finally we conclude that the use of those two metrics, borrowed from the complex systems theory, are potential and easier for measuring the object program structure.

In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures

We investigate on a possible way to connect the presence of low-complexity sequences (LCS) in DNA genomes and the non-stationary properties of base correlations. Under the hypothesis that these variations signal a change in the DNA function, we use a new technique, called non-stationarity entropic index (NSEI) method, and we prove that this technique is an efficient way to detect functional changes with respect to a random baseline. The remarkable aspect is that NSEI does not imply any training data or fitting parameter, the only arbitrarity being the choice of a marker in the sequence. We make this choice on the basis of biological information about LCS distributions in genomes. We show that there exists a correlation between changing the amount in LCS and the ratio of long- to short-range correlation.

The use of local entropy measures in edge detection for cytological image analysis.

Accurate edge detection is a fundamental problem in the areas of image processing and pattern recognition/classification. The lack of effective edge detection methods has slowed the application of image processing to many areas, in particular diagnostic cytology, and is a major factor in the lack of acceptance of image processing in service orientated pathology. In this paper, we present a two-step procedure which detects edges. Since most images are corrupted by noise and often contain artefacts, the first step is to clean up the image. Our approach is to use a median filter to reduce noise and background artefacts. The second operation is to locate image pixels which are 'information rich' by using local statistics. This step locates the regions of the image most likely to contain edges. The application of a threshold can then pin-point those pixels forming the edge of structures of interest. The procedure has been tested on routine cytologic specimens.