Harmonic measures for distributions with finite support on the mapping class group are singular

Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on PMF. Here, we show that when the initial distribution has finite support, the corresponding harmonic measure is singular with respect to the natural Lebesgue measure on PMF.Comment: 43 pages, 16 figures. Minor improvements overall, specifically Section 12. Added reference

Descriptive analytical study looking for agreement between colposcopic cervical findings and cervical exfoliative cytology

Background: To see whether cervical findings on colposcopy & reports of exfoliative cytology agree with each other according to grade of severity.Methods: This study included 306 cases. Data of PAP’s smear reports & colposcopic examination findings collected. Reports of colposcopically directed s cervical biopsy colleected wherever it was done (28). The colposcopic findings were graded according to Reid’s coloscopic index, reports of PAP’s smear classified according to Bethesda system. Data was analysed to find out any agreement.Results: The findings of colposcopy & PAP’S smear reports (n=306) showed significant agreement (p=0.0037). The findings of colposcopy & colposcopically directed cervical biopsy (n=28) were in agreement with each other. The reports of PAP’S smear & colposcopically directed cervical biopsy (n=28) showed agreement with each other.Conclusion: In India, cancer cervix is prevalent. Hence screening & early diagnosis of preinvasive lesions is very important. Colposcopic findings & pap’s smear reports have an agreement with each other. Pap’s is cheap, easily available, not needing specific training, but low sensitivity. Colposcopy is highly sensitive, costly, not available everywhere. Since they have significant agreement pap’s can be given an equivalent place, especially for screening. Its sensitivity can be increased by repeating the smear. It can be combined with colposcopy, where it is available to increase diagnostic yield

Correlation of body mass index, waist circumference and waist-hip ratio to fasting blood sugar levels in non-diabetics: an observational study

Background: Obesity is a serious health problem across the world. Obesity is an independent risk factor for diabetes and cardiac problems. Waist-hip ratio and waist circumference are better predictors of obesity and associated medical risks. The aims and objectives of study are to evaluate overweight and obesity in non-diabetics and assess correlation of BMI, WC and WHR with fasting blood sugar (FBS).Methods: A prospective study was carried out at D.Y. Patil Hospital Nerul, Navi Mumbai between November 2014- December 2014. Subjects attending the medical outpatient department (OPD) were invited to participate in this study. 200 subjects were screened, of whom 100 subjects having fasting sugar levels less than 110 mg/dL were enrolled. The subjects were matched with respect to age, BMI, waist circumference and Hip circumference and W: H ratio. BMI, WC and W:H ratio was correlated with FBS using Pearson’s correlation coefficient. Statistical significance was considered at P value<0.05.Results: It indicated 19.6% males (10/51) and 14.28% females (7/49) were overweight and 47.05% males (24/51) and 42.85% females (21/49) were obese according to BMI. 13.72% males (7/51) and 20.40% females (10/49) were overweight and 66.66% males (34/51) and 38.77% females (19/49) were obese according to WC. 5.88% males (3/51) and 4.08% females (2/49) were overweight and 94.11% males (48/51) and 91.83% females (45/49) were obese according to WHR.Conclusions: It can be concluded from this study that there is a positive correlation between BMI, Waist circumference, Waist: Hip Ratio and are important indicators of obesity to predict obesity

Information entropy as a measure of the quality of a nuclear density distribution

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various microscopic mean field approaches are also employed. It turns out that the entropy increases on going from crude phenomenological models to more sophisticated (microscopic) ones. It is concluded that the larger the information entropy, the better the quality of the nuclear density distribution. An alternative approach is also examined: the net information content i.e. the sum of information entropies in position and momentum space $S_{r}+S_{k}$. It is indicated that $S_{r}+S_{k}$ is a maximum, when the best fit to experimental data of the density and momentum distributions is attained.Comment: 12 pages, LaTex, no figures, Int. J. of Mod. Phys. E in pres

Complexity analysis of Klein-Gordon single-particle systems

The Fisher-Shannon complexity is used to quantitatively estimate the contribution of relativistic effects to on the internal disorder of Klein-Gordon single-particle Coulomb systems which is manifest in the rich variety of three-dimensional geometries of its corresponding quantum-mechanical probability density. It is observed that, contrary to the non-relativistic case, the Fisher-Shannon complexity of these relativistic systems does depend on the potential strength (nuclear charge). This is numerically illustrated for pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is analysed in various ground and excited states. It is found that the relativistic effects enhance when n and/or l are decreasing.Comment: 4 pages, 3 figures, Accepted in EPL (Europhysics Letters

Rapid topography mapping of scalar fields: Large molecular clusters

The following article appeared in Journal of Chemical Physics 137.7 (2012): 074116 and may be found at http://scitation.aip.org/content/aip/journal/jcp/137/7/10.1063/1.4746243An efficient and rapid algorithm for topography mapping of scalar fields, molecular electron density (MED) and molecular electrostatic potential (MESP) is presented. The highlight of the work is the use of fast function evaluation by Deformed-atoms-in-molecules (DAM) method. The DAM method provides very rapid as well as sufficiently accurate function and gradient evaluation. For mapping the topography of large systems, the molecular tailoring approach (MTA) is invoked. This new code is tested out for mapping the MED and MESP critical points (CP's) of small systems. It is further applied to large molecular clusters viz. (H 2O) 25, (C 6H 6) 8 and also to a unit cell of valine crystal at MP26-31G(d) level of theory. The completeness of the topography is checked by extensive search as well as applying the Poincaré-Hopf relation. The results obtained show that the DAM method in combination with MTA provides a rapid and efficient route for mapping the topography of large molecular systemsAuthors thank the Center for Development of Advanced Computing (C-DAC), Pune for financial and computational support. S.R.G. is grateful to the Department of Science and Technology (DST) for the award of J. C. Bose National Fellowship. R. López acknowledges partial funding from the CAM (S2009_PPQ-1545, LIQUORGAS) and MICINN (CTQ2010-19232). Authors are also thankful to Dr. Graeme M. Day, University of Cambridge, for providing the coordinates of unit cell of valine crystal and to Dr. V. Subramanian, CLRI, Chennai for providing some test run

Universal trend of the information entropy of a fermion in a mean field

We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $\Lambda$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \ln (\mu E +\nu)$. This relation holds for all the systems under consideration.Comment: 9 pages, latex, 6 figure

Enabling rapid and accurate construction of CCSD(T)-level potential energy surface of large molecules using molecular tailoring approach

The construction of the potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is an arduous task due to the high computational cost. In this Letter, we report the possibility of efficient construction of such a PES employing the molecular tailoring approach (MTA) on off-the-shelf hardware. The full calculation (FC) as well as MTA energies at CCSD(T)/aug-cc-pVTZ level for three test molecules, viz. acetylacetone, N-methyacetamide, and tropolone are reported. All the MTA energies are in excellent agreement with their FC counterparts (typical error being sub-millihartree) with a time advantage factor of 3 to 5. The energy barrier from the ground- to transition-state is accurately captured. Further, the accuracy and efficiency of the MTA method for estimating energy gradients at CCSD(T) level are demonstrated. This work brings out the possibility of the construction of PES for large molecules using MTA with the computational economy at a high level of theory and/or basis set

Co-operative electrostatics for understanding crown ether hydration patterns

A prototype problem in supramolecular chemistry is: Would it be possible to understand qualitative trends in hydration preocess of crown ether from simple considerations at the molecular levels? An answer is offered for the hydration of 18-crown-6 in terms of co-operative electrostatic effects. These effects are monitored by mapping the molecular electrostatic potential topography of 18-crown-6 as well as various interemediate hydrated species, followed by electrostatic modelling. All model calculations have been done at ab-initio HF/6-31G** level. The trends of these hydration patterns are in good agreement with the corresponding fully optimized ab-initio ones. Final structure of 18C6·4H2O is quite similar to the corresponding experimental crystal structure. Such an electrostatics-based method seems to be an excellent general tool for understanding weak interactions in supramolecular chemistry