Low Degeneracy Research Articles

Enhanced Wang Landau sampling of adsorbed protein conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical "temperature" that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.

Superaugmented Eccentric Distance Sum Connectivity Indices: Novel Highly Discriminating Topological Descriptors for QSAR/QSPR

Four highly discriminating fourth-generation topological indices (TIs), termed as superaugmented eccentric distance sum connectivity indices, as well as their topochemical versions (denoted by , , and ), have been conceptualized in this study. The values of these indices for all possible structures with three, four, and five vertices containing one heteroatom were computed using an in-house computer program. The proposed superaugmented eccentric distance sum connectivity topochemical indices exhibited exceptionally high discriminating power, low degeneracy, and high sensitivity toward both the presence and the relative position of heteroatom(s) for all possible structures with five vertices containing at least one heteroatom. Intercorrelation analysis revealed the absence of correlation of proposed indices with Zagreb indices and the molecular connectivity index. Subsequently, the proposed TIs were successfully utilized for the development of models for the prediction of checkpoint kinase inhibitory activity of 2-arylbenzimidazoles. A data set comprising 47 differently substituted analogs of 2-arylbenzimidazoles was selected for the study. The values of various TIs for each analog in the data set were computed using an in-house computer program. The resulting data were analyzed, and suitable models were developed through decision tree (DT), random forest (RF), and moving average analysis (MAA). The performance of the models was assessed by calculating the specificity, sensitivity, overall accuracy, and Mathew's correlation coefficient. A decision tree was constructed for the checkpoint kinase inhibitory activity to determine the importance of topological indices. The decision tree identified the proposed TIs -, - as the most important indices. The decision tree learned the information from the input data with an accuracy of 96% and correctly predicted the cross-validated (10-fold) data with an accuracy of 77%. Random forest correctly predicted the checkpoint kinase inhibitory activity with an accuracy of 83%. The single index-based models were also developed for the prediction of checkpoint kinase inhibitory activity using MAA. The accuracy of prediction of single index-based models derived through MAA was found to vary from a minimum of 90% to a maximum of 95%. Exceptionally high discriminating power, low degeneracy, and high sensitivity toward branching and presence of heteroatom of proposed indices can be of immense use in drug design, isomer discrimination, similarity/dissimilarity studies, quantitative structure activity/property relationships, lead optimization, and combinatorial library design.

Eccentric Connectivity Index: Extremal Graphs and Values

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine the leading coefficient in the asymptotic behavior.

A parametric model for fusion neutron emissivity tomography for the KN3 neutron camera at JET

A parametric model for fusion neutron emissivity is presented and applied to the KN3 neutron camera data collected during the trace tritium experiment at the Joint European Torus. This work is aimed at achieving a good compromise between accuracy of tomographic reconstruction and low model complexity. This means low numerical degeneracy and good time consistency of the results. The model is compared both with plasma simulation codes and other tomographic techniques, which use KN3 line integrated emissivity data, showing good agreement over the entire data set analysed (≈500 plasma discharges).

Exciton correlations in coupled quantum wells and their luminescence blue shift

In this paper we present a study of an exciton system where electrons and holes are confined in double quantum well structures. The dominating interaction between excitons in such systems is a dipole-dipole repulsion. We show that the tail of this interaction leads to a strong correlation between excitons and substantially affects the behavior of the system. Making use of qualitative arguments and estimates we develop a picture of the exciton-exciton correlations in the whole region of temperature and concentration where excitons exist. It appears that at low concentration degeneracy of the excitons is accompanied with strong multiparticle correlation so that the system cannot be considered as a gas. At high concentration the dipole-dipole repulsion suppresses the quantum degeneracy. As a result there exists a temperature region where the system behaves a classical liquid; such a region does not exist in case of contact interaction. We calculate the blue shift of the exciton luminescence line which is a sensitive tool to observe the exciton-exciton correlations.

Superaugmented Pendentic Indices: Novel Topological Descriptors for QSAR/QSPR

Four pendenticity based topological descriptors termed as superaugmented pendentic indices have been conceptualized in the present study. An in-house computer program was utilized to compute index values of all the possible structures (with at least one pendent vertex) containing four, five and six vertices. The sensitivity towards branching, discriminating power, degeneracy and mathematical properties of the proposed superaugmented pendentic indices were investigated. All the four proposed indices exhibited exceptionally high sensitivity towards branching, high discriminating power and extremely low degeneracy. Superaugmented pendentic index-4 (SA∫P-4) exhibited exceptionally high discriminating power of 114 in structures containing only six vertices. Statistical significance of the proposed indices was investigated using intercorrelation analysis with Wiener’s index, Balaban’s mean square distance index, molecular connectivity index, Zagreb indices (M1 and M2), superpendentic index and eccentric connectivity index. The exceptionally high sensitivity towards branching, high discriminating power amalgamated with extremely low degeneracy offer proposed indices a vast potential for isomer discrimination, similarity/dissimilarity, drug design, quantitative structureactivity/ structure-property relationships, lead optimization and combinatorial library design.

A novel representation of RNA secondary structure based on element-contact graphs

BackgroundDepending on their specific structures, noncoding RNAs (ncRNAs) play important roles in many biological processes. Interest in developing new topological indices based on RNA graphs has been revived in recent years, as such indices can be used to compare, identify and classify RNAs. Although the topological indices presented before characterize the main topological features of RNA secondary structures, information on RNA structural details is ignored to some degree. Therefore, it is necessity to identify topological features with low degeneracy based on complete and fine-grained RNA graphical representations.ResultsIn this study, we present a complete and fine scheme for RNA graph representation as a new basis for constructing RNA topological indices. We propose a combination of three vertex-weighted element-contact graphs (ECGs) to describe the RNA element details and their adjacent patterns in RNA secondary structure. Both the stem and loop topologies are encoded completely in the ECGs. The relationship among the three typical topological index families defined by their ECGs and RNA secondary structures was investigated from a dataset of 6,305 ncRNAs. The applicability of topological indices is illustrated by three application case studies. Based on the applied small dataset, we find that the topological indices can distinguish true pre-miRNAs from pseudo pre-miRNAs with about 96% accuracy, and can cluster known types of ncRNAs with about 98% accuracy, respectively.ConclusionThe results indicate that the topological indices can characterize the details of RNA structures and may have a potential role in identifying and classifying ncRNAs. Moreover, these indices may lead to a new approach for discovering novel ncRNAs. However, further research is needed to fully resolve the challenging problem of predicting and classifying noncoding RNAs.

Myriad of correlated electron effects found in the [formula omitted] family

The dilute, rare earth bearing family of RT 2 Zn 20 (R = rare earth, T = transition metal) intermetallic compounds can be tuned to a nearly ferromagnetic Fermi liquid that is closer to the Stoner limit than Pd (for R = Y, Lu and T = Fe). The submersion of moment bearing rare earths (Gd–Tm) into this highly polarizable matrix gives rise to exceptionally high temperature ferromagnetism (e.g. T C = 86 K for GdFe 2 Zn 20 ) for a compound with only one moment bearing ion out of 23 in the formula unit. In addition to this d-shell correlated electron behavior, 4f hybridization gives rise to six, new, Yb-based heavy fermion compounds: YbT 2 Zn 20 (T = Fe, Ru, Os, Co, Rh, Ir). These half dozen compounds manifest a range of Yb ion degeneracy values ( N ) for T ∼ T K , ranging from N = 4 – 8 . Not only do these compounds offer a clear testing ground for the effects of low temperature degeneracy on the correlated electron state, they also present an exceptionally clear experimental confirmation of the generalized Kadowaki–Woods formalism.

Superaugmented eccentric connectivity indices: new-generation highly discriminating topological descriptors for QSAR/QSPR modeling

New-generation highly discriminating topological descriptors, termed superaugmented eccentric connectivity indices (SAξc), have been conceptualized in the present study. The values of SAξc for all the possible structures of three, four, and five vertices were computed using an in-house computer program. The sensitivity to branching, discriminating power, and degeneracy of SAξc were investigated for all the possible structures of three, four, and five vertices and subsequently compared with those of the eccentric and augmented eccentric connectivity indices. The proposed superaugmented eccentric connectivity indices exhibited high sensitivity towards branching, exceptionally high discriminating power, and extremely low degeneracy. The superaugmented eccentric connectivity index-3 (SAξc3) exhibited an exceptionally high discriminating power of > 4000 for all possible structures containing only five vertices. The statistical significance of the proposed indices was investigated using intercorrelation analysis with Wiener’s index; Balaban’s J index (the average distance sum connectivity); the molecular connectivity index; the eccentric connectivity index; and the augmented eccentric connectivity index values. The high sensitivity to branching and exceptionally high discriminating power amalgamated with extremely low degeneracy give these indices vast potential for isomer discrimination, similarity/dissimilarity, drug design, quantitative structure–activity/structure–property relationships, lead optimization, and combinatorial library design.

A DNA oligonucleotide microarray for detecting human astrovirus serotypes

Human astroviruses have been shown in numerous studies to be an important cause of gastroenteritis in young children worldwide. The present communication addresses their characterization by use of oligonucleotide microarray hybridization. The system developed consists of an RT-PCR using primers of low degeneracy capable of detecting all eight serotypes of human astroviruses. RT-PCR products are then hybridized against a microarray consisting of short oligonucleotide probes 17–18 nucleotides in length. Cy3-labeled ssDNA targets are generated using a Cy3-labeled primer in the RT-PCR. The non-labeled strand is enzymatically digested, and the labeled target is rescued by column purification. This method of generating labeled target uses equimolar concentrations of the amplifying primers and does not compromise assay sensitivity for initial detection of the virus. Hybridization can be performed without the need for additional amplification. Although the amplicon spans a relatively conserved region of the astrovirus genome, the use of short probes enables type distinction despite such limited diversity. Probes differing by as little as a single nucleotide can be used to distinguish isolates. The microarray developed was capable of distinguishing representatives of the eight known serotypes of human astroviruses.

Predicting anti-HIV-1 activity of 6-arylbenzonitriles: Computational approach using superaugmented eccentric connectivity topochemical indices

Highly discriminating adjacency-cum-distance based topochemical indices termed as superaugmented eccentric connectivity topochemical indices for quantitative structure–activity and structure–property relationships (QSAR/QSPR) have been conceptualized in the present study. These indices were found to exhibit high sensitivity towards the presence and relative position of heteroatom(s), exceptionally high discriminating power and negligible degeneracy for all possible structures of five vertices containing one heteroatom. Utility of these indices was investigated for development of models for prediction of anti-human immunodeficiency virus (HIV)-1 activity using a data set comprising 81 differently substituted 6-arylbenzonitriles. The values of the superaugmented eccentric connectivity topochemical indices of all the analogues comprising the data set were computed using an in-house computer program. The resultant data was analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each analogue using these models which was then compared with the reported anti-HIV-1 activity. The accuracy of prediction was found to be ∼81% for all the three topochemical models. High sensitivity towards presence and relative position of heteroatom(s), exceptionally high discriminating power amalgamated with low degeneracy offer proposed topochemical indices vast potential for isomer discrimination, similarity/dissimilarity, drug design, quantitative structure–activity/structure–property relationships, lead optimization and combinatorial library design.

Six closely related YbT 2 Zn 20 (T = Fe, Co, Ru, Rh, Os, Ir) heavy fermion compounds with large local moment degeneracy

Heavy fermion compounds represent one of the most strongly correlated forms of electronic matter and give rise to low temperature states that range from small moment ordering to exotic superconductivity, both of which are often in close proximity to quantum critical points. These strong electronic correlations are associated with the transfer of entropy from the local moment degrees of freedom to the conduction electrons, and, as such, are intimately related to the low temperature degeneracy of the (originally) moment bearing ion. Here we report the discovery of six closely related Yb-based heavy fermion compounds, YbT(2)Zn(20), that are members of the larger family of dilute rare earth bearing compounds: RT(2)Zn(20) (T = Fe, Co, Ru, Rh, Os, Ir). This discovery doubles the total number of Yb-based heavy fermion materials. Given these compounds' dilute nature, systematic changes in T only weakly perturb the Yb site and allow for insight into the effects of degeneracy on the thermodynamic and transport properties of these model correlated electron systems.

Four New Topological Indices Based on the Molecular Path Code

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.

Retrogressive regime drift within a theory of emergent order

This paper explores the robustness of systems of political economy from within an emergent perspective. Robustness is a quality of the nexus of relationships that emerge within a political economy, and particular attention is given to processes of regime drift that might generate retrogression within a political economy. The central claim advanced here is that robustness is facilitated through polycentric organizational arrangements that entail high degeneracy, while fragility and the emergence of decadence is facilitated in relatively hierarchical arrangements that possess low degeneracy.

Can topological indices transmit information on properties but not on structures?

A survey of several topological indices (TIs) is provided according to the nature (integers or real numbers) of the local vertex invariants (LOVIs) and of the resulting molecular descriptor (TI). The 1st generation TIs such as the Wiener index when both the LOVIs and the TI are integers have a very high degeneracy. This fact can become an asset for the problem under discussion: when confronted with the "inverse problem" (reverse engineering) such indices lead to a combinatorial explosion of possible solutions. On the other extreme, TIs with very low degeneracy may also offer the possibility to transmit information on properties but not on structures, because they may be too difficult to lend themselves to reverse engineering in a reasonable amount of time. Several such indices are discussed: the novel second-generation index G (derived from the average distance-based connectivity index J in order to include a dependence on graph size and cyclicity), and third-generation indices such as the triplet TI denoted by DN2S(4) or the Kier-Hall index TOTOP. The intercorrelation of these indices is discussed: G is almost linearly-correlated with DN2S(4), and shows a different type of correlation with TOTOP.

Bunching, antibunching, and the Poisson limit of Bose-Einstein processes at low-degeneracy parameters

Random point processes are often classified as bunched, unbunched, or antibunched, depending on the value assumed by their variance-to-mean ratio (the Fano factor); in the low-degeneracy limit, the Fano factor of a Bose-Einstein process approaches the Poisson value of unity. This fact probably added strength to the conjecture that in the limit of zero degeneracy a Bose-Einstein process reduces to a memoryless Poisson process. After considering some statistics related both to counting and to arrival times, we have experimentally verified that a Bose-Einstein process retains its correlation properties down to values of the degeneracy parameter of the order of 0.01. It also follows that the two most common definitions of photon bunching, the one based on the Fano factor and the one based on the correlation function, are not equivalent at low degeneracy levels.

Predicting anti-HIV activity of 2,3-diaryl-1,3-thiazolidin-4-ones: computational approach using reformed eccentric connectivity index

The eccentric connectivity index, which has recently been employed successfully for the development of numerous mathematical models for the prediction of biological activities of diverse nature, has been reformed to overcome its limitations caused by degeneracy and insensitivity towards heteroatoms. The reformed eccentric connectivity index, termed the eccentric connectivity topochemical index, overcomes the limitations of the eccentric connectivity index by exhibiting very low degeneracy and displaying sensitivity to both the presence and relative position of heteroatoms without compromizing the discriminating power of the eccentric connectivity index. The relationship of the eccentric connectivity topochemical index, eccentric connectivity index and Wiener's index with regard to the anti-HIV activity of 2, 3-diaryl-1, 3-thiazolidin-4-one derivatives was subsequently investigated. The values of the eccentric connectivity topochemical index, the eccentric connectivity index and Wiener's index of each of 31 analogues comprizing the data set were computed using in-house computer program. Resultant data was analyzed and suitable models developed after identification of active ranges. Subsequently, each derivative was assigned a biological activity using these models, which was then compared with the reported anti-HIV activity. The accuracy of prediction using these models was found to vary from 81 to 90%. The proposed index offers a vast potential for virtual screening of combinatorial libraries, structure property/activity studies and drug design. [figure]. Basic structure of 2,3-diaryl-1, 3-thiazoidin-4-ones.

Possible effects of charge frustration inNaxCoO2: Bandwidth suppression, charge orders, and resurrected resonating valence bond superconductivity

Charge frustration due to further neighbor Coulomb repulsion can have dramatic effects on the electronic properties of ${\text{Na}}_{x}{\text{CoO}}_{2}$ in the full doping range. It can significantly reduce the effective mobility of the charge carriers, leading to a low degeneracy temperature ${ϵ}_{F}\ensuremath{\lesssim}T$. Such strongly renormalized Fermi liquid has rather unusual properties---from the point of view of the ordinary metals with ${ϵ}_{F}⪢T$---but similar to the properties that are actually observed in the ${\text{Na}}_{x}{\text{CoO}}_{2}$ system. For example, we show that the anomalous thermopower and Hall effect observed in ${\text{Na}}_{0.7}{\text{CoO}}_{2}$ may be interpreted along these lines. If the repulsion is strong, it can also lead to charge order; nevertheless, away from the commensurate dopings, the configurational constraints allow some mobility for the charge carriers, i.e., there remains some ``metallic'' component. Finally, the particularly strong bandwidth suppression around the commensurate $x=1∕3$ can help resurrect the resonating valence bond superconductivity, which would otherwise not be expected near this high doping. These suggestions are demonstrated specifically for a $tJ$-like model with an additional nearest-neighbor repulsion.

Detection of spatial correlations in an ultracold gas of fermions.

Spatial correlations are observed in an ultracold gas of fermionic atoms close to a Feshbach resonance. The correlations are detected by inducing spin-changing rf transitions between pairs of atoms. We observe the process in the strongly interacting regime for attractive as well as for repulsive atom-atom interactions and both in the regime of high and low quantum degeneracy. The observations are compared with a two-particle model that provides theoretical predictions for the measured rf transition rates.

Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any regularization. In the framework of the grand-canonical ensemble, we use an equivalence with a classical system of loops with random shapes, based on the Feynman-Kac path-integral representation of the quantum Gibbs factor. After systematic resummations of Coulomb divergences in the Mayer fugacity expansions of loop densities, there appears a screened potential $\phi$. It obeys an inhomogeneous Debye-H\"uckel equation with an effective screening length which depends on the distance from the wall. The formal solution for $\phi$ can be expanded in powers of the ratios of the de Broglie thermal wavelengths $\laa$'s of each species $\alpha$ and the limit of the screening length far away from the wall. In a regime of low degeneracy and weak coupling, exact analytical density profiles are calculated at first order in two independent parameters. Because of the vanishing of wave-functions close to the wall, density profiles vanish gaussianly fast in the vicinity of the wall over distances $\laa$'s, with an essential singularity in Planck constant $\hbar$. When species have different masses, this effect is equivalent to the appearance of a quantum surface charge localized on the wall and proportional to $\hbar$ at leading order. Then, density profiles, as well as the electrostatic potential drop created by the charge-density profile, also involve a term linear in $\hbar$ andwhich decays exponentially fast over the classical Debye screening length $\xid$. The corresponding contribution to the global surface charge exactly compensates the charge in the very vicinity of the surface, so that the net electric field vanishes in the bulk, as it should.