Entropy2014, 16(4), 2223-2233; doi:10.3390/e16042223 (doi registration under processing) - published online 17 April 2014 Show/Hide Abstract
Abstract: The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP).
Entropy2014, 16(4), 2204-2222; doi:10.3390/e16042204 - published online 16 April 2014 Show/Hide Abstract
Abstract: In Ni-Mn-Ga ferromagnetic shape memory alloys, Co-doping plays a major role in determining a peculiar phase diagram where, besides a change in the critical temperatures, a change of number, order and nature of phase transitions (e.g., from ferromagnetic to paramagnetic or from paramagnetic to ferromagnetic, on heating) can be obtained, together with a change in the giant magnetocaloric effect from direct to inverse. Here we present a thorough study of the intrinsic magnetic and structural properties, including their dependence on hydrostatic pressure, that are at the basis of the multifunctional behavior of Co and In-doped alloys. We study in depth their magnetocaloric properties, taking advantage of complementary calorimetric and magnetic techniques, and show that if a proper measurement protocol is adopted they all merge to the same values, even in case of first order transitions. A simplified model for the estimation of the adiabatic temperature change that relies only on indirect measurements is proposed, allowing for the quick and reliable evaluation of the magnetocaloric potentiality of new materials starting from readily available magnetic measurements.
Entropy2014, 16(4), 2184-2203; doi:10.3390/e16042184 - published online 15 April 2014 Show/Hide Abstract
Abstract: To recognize individual activities in multi-resident environments with pervasive sensors, some researchers have pointed out that finding data associations can contribute to activity recognition and previous methods either need or infer data association when recognizing new multi-resident activities based on new observations from sensors. However, it is often difficult to find out data associations, and available approaches to multi-resident activity recognition degrade when the data association is not given or induced with low accuracy. This paper exploits some simple knowledge of multi-resident activities through defining Combined label and the state set, and proposes a two-stage activity recognition method for multi-resident activity recognition. We define Combined label states at the model building phase with the help of data association, and learn Combined label states at the new activity recognition phase without the help of data association. Our two stages method is embodied in the new activity recognition phase, where we figure out multi-resident activities in the second stage after learning Combined label states at first stage. The experiments using the multi-resident CASAS data demonstrate that our method can increase the recognition accuracy by approximately 10%.
Entropy2014, 16(4), 2161-2183; doi:10.3390/e16042161 - published online 15 April 2014 Show/Hide Abstract
Abstract: We propose new measures of shared information, unique information and synergistic information that can be used to decompose the mutual information of a pair of random variables (Y, Z) with a third random variable X. Our measures are motivated by an operational idea of unique information, which suggests that shared information and unique information should depend only on the marginal distributions of the pairs (X, Y) and (X,Z). Although this invariance property has not been studied before, it is satisfied by other proposed measures of shared information. The invariance property does not uniquely determine our new measures, but it implies that the functions that we define are bounds to any other measures satisfying the same invariance property. We study properties of our measures and compare them to other candidate measures.
Entropy2014, 16(4), 2146-2160; doi:10.3390/e16042146 - published online 14 April 2014 Show/Hide Abstract
Abstract: In this work we review the literature for possible confirmation of a phenomenon that was proposed to develop when water is left to stand for some time undisturbed in closed vessels. The phenomenon has been termed thixotropy of water due to the weak gel-like behaviour which may develop spontaneously over time where ions and contact with hydrophilic surfaces seem to play important roles. Thixotropy is a property of certain gels and liquids that under normal conditions are highly viscous, whereas during mechanical processing their viscosity diminishes. We found experiments indicating water’s self-organizing properties, long-lived inhomogeneities and time-dependent changes in the spectral parameters of aqueous systems. The large-scale inhomogeneities in aqueous solutions seem to occur in a vast number of systems. Long-term spectral changes of aqueous systems were observed even though the source of radiation was switched off or removed. And water was considered to be an active excitable medium in which appropriate conditions for self-organization can be established. In short, the thixotropic phenomenon of water is further indicated by different experimental techniques and may be triggered by large-scale ordering of water in the vicinity of nucleating solutes and hydrophilic surfaces.
Entropy2014, 16(4), 2131-2145; doi:10.3390/e16042131 - published online 14 April 2014 Show/Hide Abstract
Abstract: Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ)-divergence. A (ρ,τ) -divergence generates a dually flat structure in the manifold of positive measures, as well as in the manifold of positive-definite matrices. The class is composed of decomposable divergences, which are written as a sum of componentwise divergences. Conversely, a decomposable dually flat divergence is shown to be a (ρ,τ) -divergence. A (ρ,τ) -divergence is determined from two monotone scalar functions, ρ and τ. The class includes the KL-divergence, α-, β- and (α, β)-divergences as special cases. The transformation between an affine parameter and its dual is easily calculated in the case of a decomposable divergence. Therefore, such a divergence is useful for obtaining the center for a cluster of points, which will be applied to classification and information retrieval in vision. For the manifold of positive-definite matrices, in addition to the dually flatness and decomposability, we require the invariance under linear transformations, in particular under orthogonal transformations. This opens a way to define a new class of divergences, called the (ρ,τ) -structure in the manifold of positive-definite matrices.