Further results on geometric properties of a family of relative entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

Wavelet entropy of Doppler ultrasound blood velocity flow waveforms distinguishes nitric oxide-modulated states

Wavelet entropy assesses the degree of order or disorder in signals and presents this complex information in a simple metric. Relative wavelet entropy assesses the similarity between the spectral distributions of two signals, again in a simple metric. Wavelet entropy is therefore potentially a very attractive tool for waveform analysis. The ability of this method to track the effects of pharmacologic modulation of vascular function on Doppler blood velocity waveforms was assessed. Waveforms were captured from ophthalmic arteries of 10 healthy subjects at baseline, after the administration of glyceryl trinitrate (GTN) and after two doses of N(G)-nitro-L-arginine-methyl ester (L-NAME) to produce vasodilation and vasoconstriction, respectively. Wavelet entropy had a tendency to decrease from baseline in response to GTN, but significantly increased after the administration of L-NAME (mean: 1.60 ± 0.07 after 0.25 mg/kg and 1.72 ± 0.13 after 0.5 mg/kg vs. 1.50 ± 0.10 at baseline, p < 0.05). Relative wavelet entropy had a spectral distribution from increasing doses of L-NAME comparable to baseline, 0.07 ± 0.04 and 0.08 ± 0.03, respectively, whereas GTN had the most dissimilar spectral distribution compared with baseline (0.17 ± 0.08, p = 0.002). Wavelet entropy can detect subtle changes in Doppler blood velocity waveform structure in response to nitric-oxide-mediated changes in arteriolar smooth muscle tone.

Farm income, population and farmland prices: a relative information approach

This paper uses an entropy-based information approach to determine if farmland values are more closely associated with urban pressure or farm income. The basic question is: how much information on changes in farm real estate values is contained in changes in population versus changes in returns to production agriculture? Results suggest population is informative, but changes in farmland values are more strongly associated with changes in the distribution of returns. However, this relationship is not true for every region nor does it hold over time, as for some regions and time periods changes in population are more informative. Results have policy implications for both equity and efficiency.

Transgenerational, dynamic methylation of stomata genes in response to low relative humidity

Transgenerational inheritance of abiotic stress-induced epigenetic modifications in plants has potential adaptive significance and might condition the offspring to improve the response to the same stress, but this is at least partly dependent on the potency, penetrance and persistence of the transmitted epigenetic marks. We examined transgenerational inheritance of low Relative Humidity-induced DNA methylation for two gene loci in the stomatal developmental pathway in Arabidopsis thaliana and the abundance of associated short-interfering RNAs (siRNAs). Heritability of low humidity-induced methylation was more predictable and penetrative at one locus (SPEECHLESS, entropy ≤ 0.02; χ2 < 0.001) than the other (FAMA, entropy ≤ 0.17; χ2 ns). Methylation at SPEECHLESS correlated positively with the continued presence of local siRNAs (r2 = 0.87; p = 0.013) which, however, could be disrupted globally in the progeny under repeated stress. Transgenerational methylation and a parental low humidity-induced stomatal phenotype were heritable, but this was reversed in the progeny under repeated treatment in a previously unsuspected manner.

Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.

Gaining ligand selectivity in thyroid hormone receptors via entropy

Nuclear receptors are important targets for pharmaceuticals, but similarities between family members cause difficulties in obtaining highly selective compounds. Synthetic ligands that are selective for thyroid hormone (TH) receptor beta (TR beta) vs. TR alpha reduce cholesterol and fat without effects on heart rate; thus, it is important to understand TR beta-selective binding. Binding of 3 selective ligands (GC-1, KB141, and GC-24) is characterized at the atomic level; preferential binding depends on a nonconserved residue (Asn-331 beta) in the TR beta ligand-binding cavity (LBC), and GC-24 gains extra selectivity from insertion of a bulky side group into an extension of the LBC that only opens up with this ligand. Here we report that the natural TH 3,5,3`-triodothyroacetic acid (Triac) exhibits a previously unrecognized mechanism of TR beta selectivity. TR x-ray structures reveal better fit of ligand with the TR alpha LBC. The TR beta LBC, however, expands relative to TR alpha in the presence of Triac (549 angstrom(3) vs. 461 angstrom(3)), and molecular dynamics simulations reveal that water occupies the extra space. Increased solvation compensates for weaker interactions of ligand with TR beta and permits greater flexibility of the Triac carboxylate group in TR beta than in TR alpha. We propose that this effect results in lower entropic restraint and decreases free energy of interactions between Triac and TR beta, explaining subtype-selective binding. Similar effects could potentially be exploited in nuclear receptor drug design.

The Contribution of the Activation Entropy to the Gas-Phase Stability of Modified Nucleic Acid Duplexes

Tricyclo-DNA (tcDNA) is a sugar-modified analogue of DNA currently tested for the treatment of Duchenne muscular dystrophy in an antisense approach. Tandem mass spectrometry plays a key role in modern medical diagnostics and has become a widespread technique for the structure elucidation and quantification of antisense oligonucleotides. Herein, mechanistic aspects of the fragmentation of tcDNA are discussed, which lay the basis for reliable sequencing and quantification of the antisense oligonucleotide. Excellent selectivity of tcDNA for complementary RNA is demonstrated in direct competition experiments. Moreover, the kinetic stability and fragmentation pattern of matched and mismatched tcDNA heteroduplexes were investigated and compared with non-modified DNA and RNA duplexes. Although the separation of the constituting strands is the entropy-favored fragmentation pathway of all nucleic acid duplexes, it was found to be only a minor pathway of tcDNA duplexes. The modified hybrid duplexes preferentially undergo neutral base loss and backbone cleavage. This difference is due to the low activation entropy for the strand dissociation of modified duplexes that arises from the conformational constraint of the tc-sugar-moiety. The low activation entropy results in a relatively high free activation enthalpy for the dissociation comparable to the free activation enthalpy of the alternative reaction pathway, the release of a nucleobase. The gas-phase behavior of tcDNA duplexes illustrates the impact of the activation entropy on the fragmentation kinetics and suggests that tandem mass spectrometric experiments are not suited to determine the relative stability of different types of nucleic acid duplexes.

Design concept evaluation based on rough number and information entropy theory

Concept evaluation at the early phase of product development plays a crucial role in new product development. It determines the direction of the subsequent design activities. However, the evaluation information at this stage mainly comes from experts' judgments, which is subjective and imprecise. How to manage the subjectivity to reduce the evaluation bias is a big challenge in design concept evaluation. This paper proposes a comprehensive evaluation method which combines information entropy theory and rough number. Rough number is first presented to aggregate individual judgments and priorities and to manipulate the vagueness under a group decision-making environment. A rough number based information entropy method is proposed to determine the relative weights of evaluation criteria. The composite performance values based on rough number are then calculated to rank the candidate design concepts. The results from a practical case study on the concept evaluation of an industrial robot design show that the integrated evaluation model can effectively strengthen the objectivity across the decision-making processes.

Illegal pedestrian crossing at signalised intersections : Incidence and relative risk

Illegal pedestrian behaviour is common and is reported as a factor in many pedestrian crashes. Since walking is being promoted for its health and environmental benefits, minimisation of its associated risks is of interest. The risk associated with illegal road crossing is unclear, and better information would assist in setting a rationale for enforcement and priorities for public education. An observation survey of pedestrian behaviour was conducted at signalised intersections in the Brisbane CBD (Queensland, Australia) on typical workdays, using behavioural categories that were identifiable in police crash reports. The survey confirmed high levels of crossing against the lights, or close enough to the lights that they should legally have been used. Measures of exposure for crossing legally, against the lights, and close to the lights were generated by weighting the observation data. Relative risk ratios were calculated for these categories using crash data from the observation sites and adjacent midblocks. Crossing against the lights and crossing close to the lights both exhibited a crash risk per crossing event approximately eight times that of legal crossing at signalised intersections. The implications of these results for enforcement and education are discussed, along with the limitations of the study.

The relative age effect in Australian Football League players

Youth sports teams are usually grouped into yearly age groups based on fixed cut-off date (September 1st in the UK and January 1st in Australia). Children born just after this cut-off will be the oldest and most mature in their age group. This gives them an advantage in competitive sport, an advantage which has persisted into adulthood as shown by seasonal patterns in the dates of birth of professional ice hockey, football and basketball players. We were interested in whether a similar seasonal pattern exists in professional Australian Football League (AFL) players. We examined all AFL players in the 2009 season excluding foreign-born players. We compared the observed number of players’ born in each month with the expected number based on national statistics. There was a marked and statistically significant seasonality in players’ dates of birth. There were 33% more players than expected with dates of birth in January, and 25% fewer in December. Players who are relatively older in youth AFL teams have a better chance of turning professional.