Generalized Shannon-Khinchin Axioms and Uniqueness Theorem for Pseudo-additive Entropies

We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as Sharma-Mital and Frank-Daffertshofer entropy. We provide the generalization of Shannon-Khinchin axioms and give the corresponding uniqueness theorem. The previous attempts at such axiomatizations are also discussed

A unified characterization of generalized information and certainty measures

In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously considered by numerous authors. We provide the corresponding characterization theorems and define a new generalized measure called the Inforcer, which is the quasi-linear mean of the function associated to the event probability following the general composition law. In particular, we pay attention to the polynomial composition and the corresponding polynomially composable Inforcer measure. The most common measures appearing in literature can be obtained by specific choice of parameters appearing in our generic measures and they are listed in tables

An axiomatic characterization of generalized entropies under analyticity condition

We present the characterization of the Nath, R\'enyi and Havrda-Charv\'at-Tsallis entropies under the assumption that they are analytic function with respect to the distribution dimension, unlike the the previous characterizations, which supposes that they are expandable maximized for uniform distribution

On the weighted reverse order laws for the Moore-Penrose inverse and K-inverses

The main objective of this article is to study several generalizations of the reverse order law for the Moore-Penrose inverse in ring with involution.Comment: 13 pages, original research articl

Comments on "A two-parameter generalization of Shannon-Khinchin Axioms and the uniqueness theorem"

Wada and Suyari proposed a two-parameter generalization of Shannon-Khinchin axioms (TGSK axioms) [T. Wada and H. Suyari, Physics Letters A, 368(3)]. We derive a new class of entropies which differs from Wada-Suyari's class by fixing the incorrectness which occurs in the mentioned paper. Also, we consider a two-parameter class of entropies derived from the maxent principle proposed in [Kaniadakis, G. and Lissia, M. and Scarfone, AM, Physica A: Statistical Mechanics and its Applications, 340(1)]. We rederived this class by changing initial condition, obtaining the same class as our class derived from TGSK axioms.Comment: 4 page

Entropy Message Passing

The paper proposes a new message passing algorithm for cycle-free factor graphs. The proposed "entropy message passing" (EMP) algorithm may be viewed as sum-product message passing over the entropy semiring, which has previously appeared in automata theory. The primary use of EMP is to compute the entropy of a model. However, EMP can also be used to compute expressions that appear in expectation maximization and in gradient descent algorithms.Comment: 5 pages, 1 figure, to appear in IEEE Transactions on Information Theor

Cross-correlation between the cosmic microwave and infrared backgrounds for integrated Sachs-Wolfe detection

We investigate the cross-correlation between the cosmic infrared background (CIB) and cosmic microwave background (CMB) anisotropies due to the integrated Sachs-Wolfe (ISW) effect. We first describe the CIB anisotropies using a linearly biased power spectrum, valid on the angular scales of interest. From this, we derive the theoretical angular power spectrum of the CMB-CIB cross-correlation for different instruments and frequencies. Our cross-spectra show similarities in shape with usual CMB/galaxies cross-correlations. We discuss the detectability of the ISW signal by performing a signal-to-noise (SNR) analysis with our predicted spectra. Our results show that : (i) in the ideal case of noiseless, full-sky maps, the significances obtained range from 6 to 7 sigmas depending on the frequency, with a maximum at 353 GHz (ii) in realistic cases which account for the presence of noise including astrophysical contaminents, the results depend strongly on the major contribution to the noise term. They span from 2 to 5 sigmas, the most favorable frequency for detection being 545 GHz. We also find that the joint use of all available frequencies in the cross-correlation does not improve significantly the total SNR, due to the high level of correlation of the CIB maps at different frequencies.Comment: 10 pages, 6 figures, 1 table ; small changes to match the version published in MNRA

Gradient Computation In Linear-Chain Conditional Random Fields Using The Entropy Message Passing Algorithm

The paper proposes a numerically stable recursive algorithm for the exact computation of the linear-chain conditional random field gradient. It operates as a forward algorithm over the log-domain expectation semiring and has the purpose of enhancing memory efficiency when applied to long observation sequences. Unlike the traditional algorithm based on the forward-backward recursions, the memory complexity of our algorithm does not depend on the sequence length. The experiments on real data show that it can be useful for the problems which deal with long sequences.Comment: 11 pages, 2 tables, 3 figures, 2 algorithm

Vortex configurations, matching, and domain structure in large arrays of artificial pinning centers

High-resolution scanning Hall probe microscopy has been used to image vortex configurations in very large periodic arrays of artificial pinning sites. Strong matching effects are seen at fields where either one or two vortices can sit at a site; with three vortices per site, however, no clear matching is observed. Matching effects have been also been observed at several fractional multiples of the matching field, including 1/5, 1/4, 1/3, 1/2, and 3/4. These fractional values are characterized by striking domain structure and grain boundaries.Comment: 4 pages, 5 figure

On kurtosis and extreme waves in crossing directional seas:A laboratory experiment

We examine the statistical properties of extreme and rogue wave activity in crossing directional seas, to constrain the probabilistic distributions of wave heights and wave crests in complex sea states; such crossing seas alter the statistical structure of surface waves and are known to have been involved in several marine accidents. Further, we examine the relationship between the kurtosis as an indicator of nonlinearity in the spectrum and the directionality and crossing angles of the sea-state components. Experimental tests of two-component directionally spread irregular waves with varying frequency, directional spreading and component crossing angles were carried out at the Ocean Basin Laboratory in Trondheim, Norway. The results from the experiments show that wave heights are well described by a first-order (linear) statistical distribution, while for the wave crest heights several cases exceed a second-order distribution. The number of rogue waves is relatively low overall, which agrees with previous findings in directionally spread seas. The kurtosis and wave and crest height exceedance probabilities were more affected by varying the directional spreading of the components than by varying the crossing angles between components; reducing the component directional spreading increases the kurtosis and increases the exceedance probabilities. The kurtosis can be estimated quite well for two-component seas from the directional spreading using an empirical relationship based on the two-dimensional Benjamin–Feir index when the effects of bound modes are included. This result may allow forecasting of the probability of extreme waves from the directional spreading in complex sea states