An Information Theory framework for two-stage binary image operator design

The design of translation invariant and locally defined binary image operators over large windows is made difficult by decreased statistical precision and increased training time. We present a complete framework for the application of stacked design, a recently proposed technique to create two-stage operators that circumvents that difficulty. We propose a novel algorithm, based on Information Theory, to find groups of pixels that should be used together to predict the Output Value. We employ this algorithm to automate the process of creating a set of first-level operators that are later combined in a global operator. We also propose a principled way to guide this combination, by using feature selection and model comparison. Experimental results Show that the proposed framework leads to better results than single stage design. (C) 2009 Elsevier B.V. All rights reserved.

Entanglement of Low-Energy Excitations in Conformal Field Theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst`s analysis

Hydrodynamic studies were conducted in a semi-cylindrical spouted bed column of diameter 150 mm, height 1000 mm, conical base included angle of 60 degrees and inlet orifice diameter 25 mm. Pressure transducers at several axial positions were used to obtain pressure fluctuation time series with 1.2 and 2.4 mm glass beads at U/U-ms from 0.3 to 1.6, and static bed depths from 150 to 600 mm. The conditions covered several flow regimes (fixed bed, incipient spouting, stable spouting, pulsating spouting, slugging, bubble spouting and fluidization). Images of the system dynamics were also acquired through the transparent walls with a digital camera. The data were analyzed via statistical, mutual information theory, spectral and Hurst`s Rescaled Range methods to assess the potential of these methods to characterize the spouting quality. The results indicate that these methods have potential for monitoring spouted bed operation.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

An entropy-based approach to automatic image segmentation of satellite images

An entropy-based image segmentation approach is introduced and applied to color images obtained from Google Earth. Segmentation refers to the process of partitioning a digital image in order to locate different objects and regions of interest. The application to satellite images paves the way to automated monitoring of ecological catastrophes, urban growth, agricultural activity, maritime pollution, climate changing and general surveillance. Regions representing aquatic, rural and urban areas are identified and the accuracy of the proposed segmentation methodology is evaluated. The comparison with gray level images revealed that the color information is fundamental to obtain an accurate segmentation. (C) 2010 Elsevier B.V. All rights reserved.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Adaptive Approach for a Maximum Entropy Algorithm in Ecological Niche Modeling

This paper presents an Adaptive Maximum Entropy (AME) approach for modeling biological species. The Maximum Entropy algorithm (MaxEnt) is one of the most used methods in modeling biological species geographical distribution. The approach presented here is an alternative to the classical algorithm. Instead of using the same set features in the training, the AME approach tries to insert or to remove a single feature at each iteration. The aim is to reach the convergence faster without affect the performance of the generated models. The preliminary experiments were well performed. They showed an increasing on performance both in accuracy and in execution time. Comparisons with other algorithms are beyond the scope of this paper. Some important researches are proposed as future works.

A mathematical view of biological complexity

This essay is a trial on giving some mathematical ideas about the concept of biological complexity, trying to explore four different attributes considered to be essential to characterize a complex system in a biological context: decomposition, heterogeneous assembly, self-organization, and adequacy. It is a theoretical and speculative approach, opening some possibilities to further numerical and experimental work, illustrated by references to several researches that applied the concepts presented here. (C) 2008 Elsevier B.V. All rights reserved.