Combinatorial Entropy Research Articles

Fault Diagnosis Method for Power Network Based on Combinational Cross Entropy Algorithm

A new method of fault diagnosis for power networks by using the combinatorial cross entropy (CCE) algorithm is proposed. The research contents in this paper mainly contain the two parts: transmission network fault diagnosis and distribution network fault location. For transmission network, the optimization model is built by considering the relationship among fault elements, action information of protective relays and circuit breakers. For distribution network, constructing fault location model according to the logic relationship between fault current and equipment condition. The optimal solution of two models are solved by CCE algorithm, then fault element (s) in transmission network and fault section (s) in distribution network can be identified by the optimal solution. Various fault conditions are simulated in test system and the results show that conclusions obtained by proposed method are correct, which prove CCE algorithm diagnose fault effectively.

Structural-phase transformations in a Cu3Pt alloy during atomic ordering

A complex structural-phase state is revealed by Monte Carlo investigations in a Cu3Pt alloy during the order–disorder transition, which involves atomic ordering and structural transformation. Under thermal cycling of the alloy, its plot for the difference between the free energies per atom in the disordered and partially ordered states has a hysteresis loop. An analysis of the temperature dependences of the difference between configurational energy and combinatorial entropy of a partially disordered state shows that it is the internal energy that plays the leading part rather than the system’s entropy. Under thermal cycling, there is a hysteresis loop in the region of low stability states of the system, the loops being also observed both in the configurational energy plots and those of the combinatorial entropy: under heating and cooling the system is found to be in differing structural-phase states. The region of low-stability states is noted by peculiar domain structure: a so-called tangled domain structure indicating the absence of predominating phases or domains. This tangled domain structure evidences of a thermodynamically indefinite structural state of the system, at which the symmetry of its structural components could be different. The thermodynamic stimuli of a transformation are very few, which results in a wide range of possible structural states observed in the system.

The entropic impact of tethering, multivalency and dynamic recruitment in systems with specific binding groups

This Highlight Article discusses the important yet frequently overlooked entropic effects in soft matter systems that have one or more tethered binding groups. We show that the effective interactions depend sensitively on a combination of configurational, combinatorial and translational entropy factors, which have to do with the tethering of the binding groups, the binding state multiplicity in multivalent systems, and the dynamic recruitment of surface-mobile binding groups. Importantly, these entropic effects can give rise to qualitatively new behavior, e.g. in the phase behavior of DNA-functionalized colloids or in the targeting of ligand-functionalized nanoparticles to cell receptors. A better understanding of the thermodynamics of tethered (multivalent) bond interactions thus impacts a wide range of fields, including soft materials science, biophysics, nanomedicine and biosensing, supramolecular and colloidal self-assembly, and nanofabrication.

Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order analysis in complex networks and compare the results with ordinary graph spectra. Methods and results are obtained using social network of the Zachary karate club.

STRING NUMBERS OF ABELIAN GROUPS

The string number of self-maps arose in the context of algebraic entropy and it can be viewed as a kind of combinatorial entropy function. Later on, its values for endomorphisms of abelian groups were calculated in full generality. We study its global version for abelian groups, providing several examples involving also Hopfian abelian groups. Moreover, we characterize the class of all abelian groups with string number zero in many cases and discuss its stability properties.

Risk Assessment of Gastric Cancer Caused by Helicobacter pylori Using CagA Sequence Markers

BackgroundAs a marker of Helicobacter pylori, Cytotoxin-associated gene A (cagA) has been revealed to be the major virulence factor causing gastroduodenal diseases. However, the molecular mechanisms that underlie the development of different gastroduodenal diseases caused by cagA-positive H. pylori infection remain unknown. Current studies are limited to the evaluation of the correlation between diseases and the number of Glu-Pro-Ile-Tyr-Ala (EPIYA) motifs in the CagA strain. To further understand the relationship between CagA sequence and its virulence to gastric cancer, we proposed a systematic entropy-based approach to identify the cancer-related residues in the intervening regions of CagA and employed a supervised machine learning method for cancer and non-cancer cases classification.MethodologyAn entropy-based calculation was used to detect key residues of CagA intervening sequences as the gastric cancer biomarker. For each residue, both combinatorial entropy and background entropy were calculated, and the entropy difference was used as the criterion for feature residue selection. The feature values were then fed into Support Vector Machines (SVM) with the Radial Basis Function (RBF) kernel, and two parameters were tuned to obtain the optimal F value by using grid search. Two other popular sequence classification methods, the BLAST and HMMER, were also applied to the same data for comparison.ConclusionOur method achieved 76% and 71% classification accuracy for Western and East Asian subtypes, respectively, which performed significantly better than BLAST and HMMER. This research indicates that small variations of amino acids in those important residues might lead to the virulence variance of CagA strains resulting in different gastroduodenal diseases. This study provides not only a useful tool to predict the correlation between the novel CagA strain and diseases, but also a general new framework for detecting biological sequence biomarkers in population studies.

Molecular Weight Effects on the Miscibility Behavior of Dextran and Maltodextrin with Poly(vinylpyrrolidone)

To characterize and interpret the miscibility of dextran and maltodextrin with poly(vinylpyrrolidone) (DEX-PVP) as a function of polymer molecular weights. Blend miscibility was studied using 4 different molecular weight (MW) grades of DEX combined with 5 MW grades of PVP, over a broad compositional range. Miscibility was evaluated by inspection of glass transition events measured by differential scanning calorimetry (DSC). Fourier transform mid-infrared spectroscopy (FTIR), combined with curve fitting, was performed to characterize the extent of hydrogen bonding. The observed miscibility behavior was further interpreted in terms of mixing thermodynamics. Miscibility of the blends ranged from fully miscible to completely immiscible with multiple partially miscible systems observed. Increasing polymer molecular weight decreased miscibility. For the lowest DEX grade, hydrogen bonding was independent of PVP MW, as expected since all systems were completely miscible. Higher molecular weights of DEX resulted in reduced intermolecular hydrogen bonding and decreased miscibility, increasingly so for higher MW PVP grades. Evaluation of the mixing thermodynamics supported these findings. With higher combined molecular weights of DEX-PVP blends, phase behavior evolves from completely miscible to virtually immiscible. Concurrently, DEX-PVP hydrogen bonding decreases. From a thermodynamic perspective, the combinatorial mixing entropy was observed to decrease as the molecular weight of the polymers increased, providing a reduced counterbalance to the unfavorable mixing enthalpy thought to accompany this polymer combination.

Controlling the temperature sensitivity of DNA-mediated colloidal interactions through competing linkages

We propose a new strategy to improve the self-assembly properties of DNA-functionalised colloids. The problem that we address is that DNA-functionalised colloids typically crystallize in a narrow temperature window, if at all. The underlying reason is the extreme sensitivity of DNA-mediated interactions to temperature or other physical control parameters. We propose to widen the window for colloidal crystallization by exploiting the competition between DNA linkages with different nucleotide sequences, which results in a temperature-dependent switching of the dominant bond type. Following such a strategy, we can decrease the temperature dependence of DNA-mediated self assembly to make systems that can crystallize in a wider temperature window than is possible with existing systems of DNA functionalised colloids. We report Monte Carlo simulations that show that the proposed strategy can indeed work in practice for real systems and specific, designable DNA sequences. Depending on the length ratio of the different DNA constructs, we find that the bond switching is either energetically driven (equal length or `symmetric' DNA) or controlled by a combinatorial entropy gain (`asymmetric' DNA), which results from the large number of possible binding partners for each DNA strand. We provide specific suggestions for the DNA sequences with which these effects can be achieved experimentally.

Predicting the functional impact of protein mutations: application to cancer genomics

As large-scale re-sequencing of genomes reveals many protein mutations, especially in human cancer tissues, prediction of their likely functional impact becomes important practical goal. Here, we introduce a new functional impact score (FIS) for amino acid residue changes using evolutionary conservation patterns. The information in these patterns is derived from aligned families and sub-families of sequence homologs within and between species using combinatorial entropy formalism. The score performs well on a large set of human protein mutations in separating disease-associated variants (∼19 200), assumed to be strongly functional, from common polymorphisms (∼35 600), assumed to be weakly functional (area under the receiver operating characteristic curve of ∼0.86). In cancer, using recurrence, multiplicity and annotation for ∼10 000 mutations in the COSMIC database, the method does well in assigning higher scores to more likely functional mutations (‘drivers’). To guide experimental prioritization, we report a list of about 1000 top human cancer genes frequently mutated in one or more cancer types ranked by likely functional impact; and, an additional 1000 candidate cancer genes with rare but likely functional mutations. In addition, we estimate that at least 5% of cancer-relevant mutations involve switch of function, rather than simply loss or gain of function.

Combinatorial entropies and statistics

We examine the {combinatorial} or {probabilistic} definition ("Boltzmann's principle") of the entropy or cross-entropy function $H \propto \ln \mathbb{W}$ or $D \propto - \ln \mathbb{P}$, where $\mathbb{W}$ is the statistical weight and $\mathbb{P}$ the probability of a given realization of a system. Extremisation of $H$ or $D$, subject to any constraints, thus selects the "most probable" (MaxProb) realization. If the system is multinomial, $D$ converges asymptotically (for number of entities $N \back \to \back \infty$) to the Kullback-Leibler cross-entropy $D_{KL}$; for equiprobable categories in a system, $H$ converges to the Shannon entropy $H_{Sh}$. However, in many cases $\mathbb{W}$ or $\mathbb{P}$ is not multinomial and/or does not satisfy an asymptotic limit. Such systems cannot meaningfully be analysed with $D_{KL}$ or $H_{Sh}$, but can be analysed directly by MaxProb. This study reviews several examples, including (a) non-asymptotic systems; (b) systems with indistinguishable entities (quantum statistics); (c) systems with indistinguishable categories; (d) systems represented by urn models, such as "neither independent nor identically distributed" (ninid) sampling; and (e) systems representable in graphical form, such as decision trees and networks. Boltzmann's combinatorial definition of entropy is shown to be of greater importance for {"probabilistic inference"} than the axiomatic definition used in information theory.

Hydrostatic Pressure Effect on the Phase Transitions of a Closed-Loop Type Block Copolymer by Using 2D FTIR Correlation Spectroscopy

The effect of hydrostatic pressure (P) on the phase transitions of polystyrene-block-poly(n-pentyl methacrylate) copolymer [PS-b-PnPMA] was investigated with FTIR spectroscopy at various temperatures. The experiments were performed by using a specially designed pressure cell optimized for low-pressure regime (<100 bar) with a higher resolution ( approximately 1 bar). The size of the closed loop consisting of both the lower disorder-to-order transition (LDOT) and the upper order-to-disorder transition (UODT) measured by FTIR spectroscopy becomes smaller with increasing P, consistent with results obtained from birefringence measurement. At lower temperatures with increasing P, the PS main chains are found to move before the PnPMA main chains. This is because the mobility of the PnPMA main chains is restricted due to the cluster formation of the alkyl side chain. At higher temperatures, the PnPMA block chains are more mobile than the PS block chains due to their larger specific volumes. The results indicate that the LDOT is mainly affected by a favorable directional interaction between PS and PnPMA blocks due to the cluster formation of the alkyl side chain, whereas the UODT depends on the combinatorial entropy.

The Combinatorial Diagnostic Entropy and Symptoms' Informativity

The Combinatorial Diagnostic Entropy and Symptoms' InformativityThis paper presents combinatorial measures of the system condition uncertainty (diagnostic entropy) and the diagnostic symptoms' informativity. The multi-valued diagnostic model has been assumed. Proposed measures can be used in the manner similar to Shannon entropy use for the diagnostic model analysis and the diagnostic algorithm planning process.

Compression of partially defined information

For partially defined (fuzzy) data we investigate the optimal coding that permits reconstructing some crispification of the data from the code. The combinatorial entropy is obtained for the class of partially defined sequences with given parameters and a coding theorem is proved for fuzzy information sources. The properties of the corresponding entropy are studied and compared with the properties of Shannon entropy.

Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses

Conventional equilibrium statistical mechanics of open gravitational systems is known to be problematical. We first recall that spherical stars/galaxies acquire unbounded radii, become infinitely massive, and evaporate away continuously if one uses the standard Maxwellian distribution fB (which maximizes the usual Boltzmann‐Shannon entropy and hence has a tail extending to infinity). Next, we show that these troubles disappear automatically if we employ the exact most probable distribution f (which maximizes the combinatorial entropy and hence possesses a sharp cutoff tail). Finally, if astronomical observation is carried out on a large galaxy, then the Poisson equation together with thermal de Broglie wavelength provides useful information about the cutoff radius rK, cutoff energy εK, and the huge quantum number K up to which the cluster exists. Thereby, a refinement over the empirical lowered isothermal King models, is achieved. Numerically, we find that the most probable distribution (MPD) prediction fits well the number density profile near the outer edge of globular clusters.

Numerical calculation of the combinatorial entropy of partially ordered ice

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case, corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for other systems.

Miscibility of branched polycarbonate blends with poly(ethylene-co-1,4-dimethyl cyclohexane terephthalate) copolyesters

The phase behavior of branched polycarbonate (BPC) blends with poly(ethylene terephthalate-co-1,4-dimethyl cyclohexane terephthalate) copolyesters (PECT), as well as their rheological properties, were assessed. Even though BPC blends with PECT prepared by solvent casting proved to be immiscible, BPC and PECT copolyesters containing 1,4-dimethyl cyclohexane (CHDM) from 32 to 80 mole% formed homogeneous mixtures upon heating. The homogenization temperatures of the blends decreased with increasing CHDM content in PECT. The interaction energies of the BPC-PECT pairs calculated from the phase boundary in accordance with the lattice-fluid theory were positive and also decreased with increasing CHDM content in PECT. It was shown that the phase homogenization of these blends occurs upon heating when the combinatorial entropy term, which is favorable for miscibility, overcomes unfavorable energetic terms at elevated temperatures. A novel product, which is not limited by the drawbacks of linear polycarbonate (PC) and evidences processability superior to that of the PC/PECT blends, can be developed via the blending of BPC and PECT.

Phase behavior predictions for polymer blends containing reversibly associating endgroups

AbstractA mean field model is developed to predict how polymer–polymer miscibility changes if polymers are functionalized with noncovalent, reversibly binding endgroups. The free‐energy model is based on the Flory–Huggins mixing theory and has been modified using Painter's association model to account for equilibrium self‐association of endgroups. Model input parameters include the length of polymer chains, a temperature‐dependent interaction parameter, and a temperature‐dependent equilibrium constant for each type of associating endgroup. The analysis is applied to 12 possible blend combinations involving self‐complementary interactions and seven combinations involving hetero‐complementary [i.e. donor–acceptor (DA)] interactions. Combinations involve both monofunctional and telechelic associating chains. Predicted phase diagrams illustrate how self‐complementary interactions can stabilize two‐phase regions and how DA interactions can stabilize single phase regions. The model is a useful tool in understanding the delicate balance between the combinatorial entropy of mixing polymer chains, the repulsive interactions between dissimilar polymers, and the additional enthalpic and entropic changes due to end‐group association of chain ends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3285–3299, 2007

Thermodynamics of liquid-crystalline solutions of hydroxypropyl cellulose in water and ethanol

Phase diagrams were constructed and comprehensive thermodynamic analysis was performed for hydroxypropyl cellulose-water and hydroxypropyl cellulose-ethanol systems with the use of the static sorption, calorimetry, cloud-point, polarization microscopy, and X-ray diffraction analysis techniques and the measurement of transmitted polarized light intensity. The concentration dependences of the enthalpy, entropy, and Gibbs energy of the formation of liquid-crystalline phases in the systems were determined. It was found that the formation of liquid-crystalline solutions of hydroxypropyl cellulose in water is associated with the energy term of interaction between the components and that in ethanol solutions is due to changes in combinatorial entropy.

Ternary Polymer Solutions with Hydrogen Bonds, 1

AbstractThe Flory Huggins methodology coupled to AET has been extended to ternary polymer systems, in particular to solvent (A)/polymer 1 (B)/polymer 2 (C) systems, with the two polymers displaying H‐bonding interactions. Because the H‐bonding can perturb the randomness of polymeric conformations, the change in Gibbs free energy of mixing, ΔG, should arise from changes in combinatorial entropy as well as in interaction energy. The combinatorial part of ΔG is evaluated through AET as a function of the association constant η between B and C components, the autoassociation constant σ between B components, and the independent number m of interaction sites of acceptor C. The enthalpic contribution is evaluated by introducing concentration independent interaction parameters, $g'_{ij}$, evaluated by subtracting from the functions gij(ϕ) the energetic contributions due to the H‐bonding specific interactions. Once the resulting ΔG equation is tested, values obtained for hypothetic systems with low, moderate and strong H‐bonding interactions are discussed.magnified image

A remark on the topological entropies of covers and partitions

We study if the combinatorial entropy of a finite cover can be computed using finite partitions finer than the cover. This relates to an unsolved question in [R] for open covers. We explicitly compute the topological entropy of a fixed clopen cover showin