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PubMed2002

Mapping of sp2/sp3 in DLC thin film by signal processed ESI series energy-loss image.

A set of signal processing methods comprising fast Fourier transform interpolation, maximum entropy deconvolution and wavelet transformation has been successfully integrated to improve the equality of the extracted C K-edge spectra from electron spectroscopic imaging (ESI) series. Fast Fourier transform interpolation is used to improve the dispersion arising from discrete sampling of ESI series in the energy space. The maximum entropy method is used to dispel the convolution effect resulting from that ESI series acquired with a finite energy window. Wavelet transformation is applied to de-noise the extracted ESI spectrum. The post-processed ESI spectrum has quality as good as that of a probe-acquired spectrum and makes semi-quantitative analysis of the two-dimensional sp2/sp3 ratio map in diamond-like carbon thin film possible. In general, this method is applicable for reconstructing good quality core-loss electron energy-loss spectra from a nanometre-sized area, so that it may be possible to quantitatively analyse two-dimensional information about electronic structure in materials with near nanometre resolution.

Journal Article↗

PubMed2003

Variational formula for the free energy based on incomplete sampling in a molecular simulation.

Finite sampling in free-energy perturbation (FEP) calculations by molecular simulation leads to reproducible systematic errors, with sign shown to depend (in a known way) only on which system governs sampling in the simulation. Thus the result of a FEP calculation can be used as a bound on the true free energy. This inequality is of a wholly different nature from established forms such as the Gibbs-Bogoliubov inequality or the second law, in that its origins relate to the performance of a molecular simulation. If one can identify a suitable reference system having a free energy known as a function of some defining parameter, variational schemes based on the finite-sampling inequalities can be implemented. This idea is demonstrated through calculation of the free energy of a hard-sphere solid by perturbing from harmonic references and of a hard-sphere fluid by perturbing from infinitely polydisperse references. The tightness of the bounds increases with the amount of sampling in the simulation and correlates with the entropy difference between the target and reference systems. The bounds are tightest near the point where the entropy difference is least.

Journal Article↗

PubMedDate not supplied

Predictive performance of anthropometric indexes of central obesity for the risk of type 2 diabetes.

BACKGROUND: In spite of several available anthropometric indexes, the relative merit of these indexes for the prediction of type 2 diabetes remains unknown. Considering that obesity and diabetes commonly coexist as co-morbidities, our objective was to directly compare the performance of measures of central and general obesity to predict the risk of type 2 diabetes. METHODS: We conducted a case-control study of type 2 diabetes on 150 cases and 150 age- and gender-matched controls. We directly compared the predictive performance of five anthropometric indexes: four related to central obesity--waist circumference (WC), waist/hip ratio (WHR), abdominal volume index (AVI) and conicity index (CI); and one related to general obesity--body mass index (BMI). We used various statistical approaches like area under (AUC) receiver-operating characteristic (ROC) curves, likelihood ratios, logistic regression and Shannon's entropy to compare the performance of the indexes in the study sample as well as bootstrapped samples. RESULTS: WC had the highest overall predictive accuracy that was gender insensitive (AUC=0.77 in males and 0.74 in females); a comparable information content as that of AVI (Shannon's entropy=1.81 for WC and 1.84 for AVI) and was a better predictor of the risk of type 2 diabetes than all the remaining indexes. WC also correlated strongly with the biochemical markers of diabetes like blood sugar and lipid profile. CONCLUSIONS: WC is a simple, non-invasive and accurate predictor of the risk of type 2 diabetes that can potentially be used in screening programs in developing countries.

Adult↗

PubMed2004

Gradient-based manipulation of nonparametric entropy estimates.

This paper derives a family of differential learning rules that optimize the Shannon entropy at the output of an adaptive system via kernel density estimation. In contrast to parametric formulations of entropy, this nonparametric approach assumes no particular functional form of the output density. We address problems associated with quantized data and finite sample size, and implement efficient maximum likelihood techniques for optimizing the regularizer. We also develop a normalized entropy estimate that is invariant with respect to affine transformations, facilitating optimization of the shape, rather than the scale, of the output density. Kernel density estimates are smooth and differentiable; this makes the derived entropy estimates amenable to manipulation by gradient descent. The resulting weight updates are surprisingly simple and efficient learning rules that operate on pairs of input samples. They can be tuned for data-limited or memory-limited situations, or modified to give a fully online implementation.

Algorithms↗

PubMed2001

NMR relaxation studies of the role of conformational entropy in protein stability and ligand binding.

Recent advances in the measurement and analysis of protein NMR relaxation data have made it possible to characterize the dynamical properties of many backbone and side chain groups. With certain caveats, changes in flexibility that occur upon ligand binding, mutation, or changes in sample conditions can be interpreted in terms of contributions to conformational entropy. Backbone and side chain flexibility can either decrease or increase upon ligand binding. Decreases are often associated with "enthalpy-entropy compensation" and "induced fit" binding, whereas increases in conformational entropy can contribute to stabilization of complexes. In certain cases, conformational entropy appears to play a role in cooperative binding and enzyme catalysis. In addition, variations in conformational entropy and heat capacity may both be important in stabilizing the folded structures of proteins.

Entropy↗

PubMed2006

Nonparametric supervised learning by linear interpolation with maximum entropy.

Nonparametric neighborhood methods for learning entail estimation of class conditional probabilities based on relative frequencies of samples that are "near-neighbors" of a test point. We propose and explore the behavior of a learning algorithm that uses linear interpolation and the principle of maximum entropy (LIME). We consider some theoretical properties of the LIME algorithm: LIME weights have exponential form; the estimates are consistent; and the estimates are robust to additive noise. In relation to bias reduction, we show that near-neighbors contain a test point in their convex hull asymptotically. The common linear interpolation solution used for regression on grids or look-up-tables is shown to solve a related maximum entropy problem. LIME simulation results support use of the method, and performance on a pipeline integrity classification problem demonstrates that the proposed algorithm has practical value.

Algorithms↗

PubMed1997

Entropy in protein folding and in protein-protein interactions.

The reduction of conformational entropy is a major barrier that has to be overcome in protein folding and binding. Changes in solvent entropy are also a major factor. Recent advances include clarification of the fundamental issues concerning the separation of entropy into components, the treatment of association entropy in binding, and the role of size and shape effects in solvation entropy. Advances in the application of entropy calculations include an emerging consensus for estimates of backbone and sidechain entropy loss in protein folding via use of numerically intensive methods for sampling, and use of the expanding protein-structure database.

Algorithms↗

PubMed2000

Configurational entropy and diffusivity of supercooled water

As a liquid approaches the glass transition, its properties are dominated by local potential minima in its energy landscape. The liquid experiences localized vibrations in the basins of attraction surrounding the minima, and rearranges via relatively infrequent inter-basin jumps. As a result, the liquid dynamics at low temperature are related to the system's exploration of its own configuration space. The 'thermodynamic approach' to the glass transition considers the reduction in configuration space explored as the system cools, and predicts that the configurational entropy (a measure of the number of local potential energy minima sampled by the liquid) is related to the diffusion constant. Here we report a stringent test of the thermodynamic approach for liquid water (a convenient system to study because of an anomalous pressure dependence in the diffusion constant). We calculate the configurational entropy at points spanning a large region of the temperature-density plane, using a model that reproduces the dynamical anomalies of liquid water. We find that the thermodynamic approach can be used to understand the characteristic dynamic anomalies, and that the diffusive dynamics are governed by the configurational entropy. Our results indicate that the thermodynamic approach might be extended to predict the dynamical behaviour of supercooled liquids in general.

Journal Article↗

PubMed2006

Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a "free volume" (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2-3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed.

Biophysical Phenomena↗

PubMed2001

Hyperleptinemia in women with Cushing's disease is driven by high-amplitude pulsatile, but orderly and eurhythmic, leptin secretion.

The episodicity of 24 h leptin release was studied in seven women (mean age 39 years, range 22-56 years) with pituitary-dependent hypercortisolism and in seven age- and body mass index (BMI)-matched female controls. Pulsatile leptin release was quantified by model-free cluster analysis and deconvolution, the orderliness of leptin patterns by the approximate entropy statistic (ApEn), and nyctohemeral leptin rhythmicity by cosinor analysis. Blood samples were taken at 10 min intervals for 24 h. Both cluster and deconvolution analysis revealed 2.4-fold increased leptin secretion in patients, caused by combined and equal amplification of basal and pulsatile secretion. Cluster analysis identified 7.1+/-1.5 peaks per 24 h in patients and 6.0+/-0.5 in controls (not significant). The statistical distribution of the individual sample secretory rates was similarly skewed in patients and controls (0.55+/-0.12 vs 0.52+/-0.07). The acrophase (timing of the nyctohemeral leptin peak) in patients occurred at 2314 h (+/-76 min) and at 0058 h (+/-18 min) in controls (not significant). The approximate entropy of leptin release was equivalent in patients and controls (1.67+/-0.03 vs 1.61+/-0.05). The approximate entropy (ApEn) for cortisol in patients was 1.53+/-0.09 and in controls was 0.93+/-0.07 (P<0.0005). Cross-ApEn showed significant pattern synchrony between leptin and cortisol release, which (unexpectedly) was not disrupted by the cortisol excess (patients, 2.02+/-0.04; controls, 1.88+/-0.09; P=0.233). Insulin levels in fasting patients ('fasting insulin') were 27+/-5.7 mU/l vs 14+/-1.6 mU/l in controls (P=0.035). Leptin secretion correlated with fasting insulin levels (R(2)=0.34, P=0.028) and with the cortisol production rate (R(2)=0.33, P=0.033) when patients and controls were combined. In summary, Cushing's disease in women increases leptin production about twofold in an amplitude-specific way. The pulse-generating, nyctohemeral phase-determining, and entropy-control mechanisms that govern the 24 h leptin release are not altered. The increased secretion is not explained by BMI and is probably only partly explained by increased insulin production, suggesting a cortisol-dependent change in adipose leptin secretion.

Adult↗

PubMed2001

Processing algorithms for tracking speckle shifts in optical elastography of biological tissues.

Parametric and nonparametric data processing schemes for analyzing translating laser speckle data used to investigate the mechanical behavior of biological tissues are examined. Cross-correlation, minimum mean square estimator, maximum likelihood, and maximum entropy approaches are discussed and compared on speckle data derived from cortical bone samples undergoing dynamic loading. While it was not the purpose of this paper to demonstrate that one processing technique is superior to another, maximum likelihood and maximum entropy approaches are shown to be particularly useful when the observed speckle motion is small.

Algorithms↗

PubMed2004

Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: application to liquid argon and water.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy S and free energy F by analyzing Boltzmann samples obtained by Monte Carlo or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). At each step of the process the system is divided into two parts, the already treated molecules (the "past"), which are fixed, and the as yet unspecified (mobile) "future" molecules. Obtaining the TP exactly requires calculating partition functions over all positions of the future molecules in the presence of the frozen past, thus it is customary to invoke various approximations to best represent these quantities. In a recent publication [Proc. Natl. Acad. Sci. USA 101, 9235 (2004)] we developed a version of HS called complete HSMC, where each TP is calculated from an MC simulation involving all of the future molecules (the complete future); the method was applied very successfully to Lennard-Jones systems (liquid argon) and a box of TIP3P water molecules. In its basic implementation the method provides lower and upper bounds for F, where the latter can be evaluated only for relatively small systems. Here we introduce a new expression for an upper bound, which can be evaluated for larger systems. We also propose a new exact expression for F and verify its effectiveness. These free energy functionals lead to significantly improved accuracy (as applied to the liquid systems above) which is comparable to our thermodynamic integration results. We formalize and discuss theoretical aspects of HSMC that have not been addressed in previous studies. Additionally, several functionals are developed and shown to provide the free energy through the analysis of a single configuration.

Argon↗

PubMed1992

Quantal analysis using maximum entropy noise deconvolution.

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Algorithms↗

PubMed2003

Additive partition of parametric information and its associated beta-diversity measure.

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type alpha. In this way, a parametric measure of beta-diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's beta-diversity for data on species relative abundances.

Biomass↗

PubMed2006

Context based error modeling for lossless compression of EEG signals using neural networks.

Two-stage lossless data compression methods involving predictors and encoders are well known. This paper discusses the application of context based error modeling techniques for neural network predictors used for the compression of EEG signals. Error modeling improves the performance of a compression algorithm by removing the statistical redundancy that exists among the error signals after the prediction stage. In this paper experiments are carried out by using human EEG signals recorded under various physiological conditions to evaluate the effect of context based error modeling in the EEG compression. It is found that the compression efficiency of the neural network based predictive techniques is significantly improved by using the error modeling schemes. It is shown that the bits per sample required for EEG compression with error modeling and entropy coding lie in the range of 2.92 to 6.62 which indicates a saving of 0.3 to 0.7 bits compared to the compression scheme without error modeling.

Data Compression↗

PubMed2002

Pulsatile, nyctohemeral and entropic characteristics of GH secretion in adult GH-deficient patients: selectively decreased pulsatile release and increased secretory disorderliness with preservation of diurnal timing and gender distinctions.

INTRODUCTION: The present clinical investigation uses a high-precision GH immunofluorometric assay to examine the postulate that principally the amplitude mode of GH secretory control is disrupted in adults with GH deficiency. PATIENTS AND METHODS: To this end, we investigated GH secretory dynamics in a cohort of 19 adult GH-deficient (GHD) patients and 19 age-, gender- and body mass index-matched controls. GHD was established by blunted (< 7 mU/l) GH release during insulin-induced hypoglycaemia. Twenty-four-hour serum GH concentration profiles obtained by 10-min sampling were analysed by deconvolution, cosinor analysis and approximate entropy to appraise pulsatile, diurnally rhythmic, and pattern-dependent GH secretion, respectively. RESULTS: Deconvolution analysis revealed that pulsatile GH release was decreased by threefold, due to amplitude-specific damping, detectable GH secretory burst frequency was paradoxically increased by twofold, but basal non-pulsatile GH release was fully preserved. GH half-life in patients and controls was similar, thus excluding major kinetic differences. The acrophase (time of maximum) of the 24-h GH rhythm was unchanged. The regularity of the GH release process, as measured by ApEn, was decreased profoundly in GHD patients (P < 10(-8)). The changes in GH secretion were similar in irradiated and nonirradiated patients. Daily GH secretion was also comparable in male and female GHD patients, but plasma IGF-I concentrations were higher in male than female patients (P = 0.031). Furthermore, the gender-specific GH ApEn difference, evident in controls, was still demonstrable in patients (P = 0.017). The ratio of plasma IGF-I and pulsatile GH production was increased threefold in patients (P = 0.004), pointing to increased sensitivity to GH in GH deficiency and/or non-GH-dependent IGF-I production. CONCLUSIONS: The present detailed analyses of daily GH secretory dynamics in patients with (moderate) GH deficiency document an amplitude-specific decrease in pulsatile GH secretion, which is partly compensated for by increased GH pulse frequency. The remarkably disorderly patterns of GH secretion in patients identify other major alterations in GH neuroregulation in such individuals, reflecting withdrawal of expected GH and/or IGF-I repression of pulsatile GH secretion. Preservation of the nyctohemeral timing of GH release and the gender contrast in GH ApEn in GHD patients would also be consistent with partial retention of central neuroregulation and GH/IGF-I feedback-dependent control in hypopituitary subjects.

Adult↗

PubMed2005

Energy landscapes and properties of biomolecules.

Thermodynamic and dynamic properties of biomolecules can be calculated using a coarse-grained approach based upon sampling stationary points of the underlying potential energy surface. The superposition approximation provides an overall partition function as a sum of contributions from the local minima, and hence functions such as internal energy, entropy, free energy and the heat capacity. To obtain rates we must also sample transition states that link the local minima, and the discrete path sampling method provides a systematic means to achieve this goal. A coarse-grained picture is also helpful in locating the global minimum using the basin-hopping approach. Here we can exploit a fictitious dynamics between the basins of attraction of local minima, since the objective is to find the lowest minimum, rather than to reproduce the thermodynamics or dynamics.

Algorithms↗

PubMed2006

Elevations in local gamma activity are accompanied by changes in the firing rate and information coding capacity of neurons in the region of the subthalamic nucleus in Parkinson's disease.

Local field potential (LFP) gamma (55-95 Hz) activity has been recorded in the vicinity of the subthalamic nucleus with both microelectrodes and macroelectrodes in patients with Parkinson's disease undergoing functional neurosurgery. Although this activity increases with movement its functional significance remains unknown. We hypothesised that elevations in local gamma activity might be associated with an increase in the capacity of individual spike trains to code information. Changes in the median firing frequency, entropy and baud were determined during spontaneous variations in the level of simultaneously recorded LFP gamma activity in a sample of 31 neurons. The latter were recorded from the zona incerta (n = 5) and subthalamic nucleus (n = 26) in 10 parkinsonian patients. Although 19% of neurons showed a decrease in firing rate, overall there was a net increase in spike frequency and baud of 18.0+/-5.5% and 16.9+/-5.3%, when periods of high gamma were compared to periods of low gamma LFP activity. In contrast, entropy dropped by only 0.8+/-0.2% across the sampled neuronal population during periods of high gamma. All net changes were significant. We conclude that overall there was a net elevation in firing rate and potential information coding capacity, assessed in terms of baud, amongst neurons during periods of elevated gamma LFP activity in the subthalamic region.

Action Potentials↗