The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Suitability of GRIND-based principal properties for the description of molecular similarity and ligand-based virtual screening

The information provided by the alignment-independent GRid Independent Descriptors (GRIND) can be condensed by the application of principal component analysis, obtaining a small number of principal properties (GRIND-PP), which is more suitable for describing molecular similarity. The objective of the present study is to optimize diverse parameters involved in the obtention of the GRIND-PP and validate their suitability for applications, requiring a biologically relevant description of the molecular similarity. With this aim, GRIND-PP computed with a collection of diverse settings were used to carry out ligand-based virtual screening (LBVS) on standard conditions. The quality of the results obtained was remarkable and comparable with other LBVS methods, and their detailed statistical analysis allowed to identify the method settings more determinant for the quality of the results and their optimum. Remarkably, some of these optimum settings differ significantly from those used in previously published applications, revealing their unexplored potential. Their applicability in large compound database was also explored by comparing the equivalence of the results obtained using either computed or projected principal properties. In general, the results of the study confirm the suitability of the GRIND-PP for practical applications and provide useful hints about how they should be computed for obtaining optimum results.

Mapping the structural core of human cerebral cortex.

Structurally segregated and functionally specialized regions of the human cerebral cortex are interconnected by a dense network of cortico-cortical axonal pathways. By using diffusion spectrum imaging, we noninvasively mapped these pathways within and across cortical hemispheres in individual human participants. An analysis of the resulting large-scale structural brain networks reveals a structural core within posterior medial and parietal cerebral cortex, as well as several distinct temporal and frontal modules. Brain regions within the structural core share high degree, strength, and betweenness centrality, and they constitute connector hubs that link all major structural modules. The structural core contains brain regions that form the posterior components of the human default network. Looking both within and outside of core regions, we observed a substantial correspondence between structural connectivity and resting-state functional connectivity measured in the same participants. The spatial and topological centrality of the core within cortex suggests an important role in functional integration.

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases.

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.

Topological locking restrains replication fork reversal.

Two-dimensional agarose gel electrophoresis, psoralen cross-linking, and electron microscopy were used to study the effects of positive supercoiling on fork reversal in isolated replication intermediates of bacterial DNA plasmids. The results obtained demonstrate that the formation of Holliday-like junctions at both forks of a replication bubble creates a topological constraint that prevents further regression of the forks. We propose that this topological locking of replication intermediates provides a biological safety mechanism that protects DNA molecules against extensive fork reversals.

Mortality associated with diabetes mellitus in comparison with history of cardiovascular disease in older women.

BACKGROUND: Women with diabetes mellitus have an increased risk of cardiovascular disease (CVD) mortality and current treatment guidelines consider diabetes to be equivalent to existing CVD, but few data exist about the relative importance of these risk factors for total and cause-specific mortality in older women. METHODS: We studied 9704 women aged ≥65 years enrolled in a prospective cohort study (Study of Osteoporotic Fractures) during a mean follow-up of 13 years and compared all-cause, CVD and coronary heart disease (CHD) mortality among non-diabetic women without and with a prior history of CVD at baseline and diabetic women without and with a prior history of CVD. Diabetes mellitus and prior CVD (history of angina, myocardial infarction or stroke) were defined as self-report of physician diagnoses. Cause of death was adjudicated from death certificates and medical records when available (>95% deaths confirmed). Ascertainment of vital status was 99% complete. Log-rank tests for the rates of death and multivariate Cox hazard models adjusted for age, smoking, physical activity, systolic blood pressure, waist girth and education were used to compare mortality among the four groups with non-diabetic women without CVD as the referent group. Results are reported as adjusted hazard ratios (HR) with 95% confidence intervals (CI). RESULTS: At baseline mean age was 71.7±5.3 years, 7.0% reported diabetes mellitus and 14.5% reported prior CVD. 4257 women died during follow-up, 36.6% were attributed to CVD. The incidence of CVD death per 1000 person-years was 9.9 and 21.6 among non-diabetic women without and with CVD, respectively, and 23.8 and 33.3 among diabetic women without and with CVD, respectively. Compared to nondiabetic women without prior CVD, the risk of CVD mortality was elevated among both non-diabetic women with CVD (HR=1.82, CI: 1.60-2.07, P<0.001) and diabetic women without prior CVD (HR=2.24, CI: 1.87-2.69, P<0.001). CVD mortality was highest among diabetic women with CVD (HR=3.41, CI: 2.61-4.45, P<0.001). Compared to non-diabetic women with CVD, diabetic women without prior CVD had a significantly higher adjusted HR for total and CVD mortality (P<0.001 and P<0.05 respectively). CHD mortality did not differ significantly between non-diabetic women with CVD and diabetic women without prior CVD. CONCLUSION: Older diabetic women without prior CVD have a higher risk of all-cause and CVD mortality and a similar risk of CHD mortality compared to non-diabetic women with pre-existing CVD. For older women, these data support the equivalence of prior CVD and diabetes mellitus in current guidelines for the prevention of CVD.

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Class of correlated random networks with hidden variables

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

In vivo assessment of use-dependent brain plasticity--beyond the "one trick pony" imaging strategy.

This article has been written as a comment to Dr Thomas and Dr Baker's article "Teaching an adult brain new tricks: A critical review of evidence for training-dependent structural plasticity in humans". We deliberately expand on the key question about the biological substrates underlying use-dependent brain plasticity rather than reiterating the authors' main points of criticism already addressed in more general way by previous publications in the field. The focus here is on the following main issues: i) controversial brain plasticity findings in voxel-based morphometry studies are partially due to the strong dependency of the widely used T1-weighted imaging protocol on varying magnetic resonance contrast contributions; ii) novel concepts in statistical analysis allow one to directly infer topological specificity of structural brain changes associated with plasticity. We conclude that iii) voxel-based quantification of relaxometry derived parameter maps could provide a new perspective on use-dependent plasticity by characterisation of brain tissue property changes beyond the estimation of volume and cortical thickness changes. In the relevant sections we respond to the concerns raised by Dr Thomas and Dr Baker from the perspective of the proposed data acquisition and analysis strategy.

Inhibitory effect of DNA supercoiling on DNA knotting

Using numerical simulations we investigated the effect of DNA supercoiling on the topological equilibrium of DNA molecules. We showed that under the steady state conditions that maintain the same effective deficit of the linking number in unknotted and knotted DNA molecules the topological equilibrium results in a much smaller fraction of knots than in the case of torsionally relaxed DNA molecules. Based on these results we propose that one of the important functions of DNA supercoiling is to reduce formation of DNA knots.

The career indecision profile : measurement equivalence in two international samples

This study tested for the measurement equivalence of a four-factor measure of career indecision (Career Indecision Profile-65 [CIP-65]) between a U.S. sample and two international samples; one composed of French-speaking young adults from France and Switzerland and the other of Italian ado- lescents. Previous research had supported the four-factor structure of the CIP-65 in both the United States and Iceland but also showed that items on two of the four scales may be interpreted differently by young adults growing up in these two countries. This study extends previous research by testing whether the four CIP-65 factors are measured equivalently in two additional international samples. Results largely supported the configural and metric invariance of the CIP-65 in the United States and international samples, but several scales showed a lack of scalar invariance. Some explanations are offered for these findings along with suggestions for future research and implications for practice.

Quantitative comparison between simulations of seismic wave propagation in heterogeneous poro-elastic media and equivalent visco-elastic solids for marine-type environments

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes an important seismic attenuation mechanism in porous rocks. As a consequence, centimetre-scale perturbations of the rock physical properties should be taken into account for seismic modelling whenever detailed and accurate responses of specific target structures are desired, which is, however, computationally prohibitive. A convenient way to circumvent this problem is to use an upscaling procedure to replace each of the heterogeneous porous media composing the geological model by corresponding equivalent visco-elastic solids and to solve the visco-elastic equations of motion for the inferred equivalent model. While the overall qualitative validity of this procedure is well established, there are as of yet no quantitative analyses regarding the equivalence of the seismograms resulting from the original poro-elastic and the corresponding upscaled visco-elastic models. To address this issue, we compare poro-elastic and visco-elastic solutions for a range of marine-type models of increasing complexity. We found that despite the identical dispersion and attenuation behaviour of the heterogeneous poro-elastic and the equivalent visco-elastic media, the seismograms may differ substantially due to diverging boundary conditions, where there exist additional options for the poro-elastic case. In particular, we observe that at the fluid/porous-solid interface, the poro- and visco-elastic seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an important result which has potentially far-reaching implications for wave-equation-based algorithms in exploration geophysics involving fluid/porous-solid interfaces, such as, for example, wavefield decomposition.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.