On the giant magnon and spike solutions for strings on AdS3×_3\times S3^3

We study solutions for the rotating strings on the sphere with a background NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of magnon and single spike solutions on R$\times$S$^2$ in the presence of constant magnetic field as two limiting cases. We also study the solution for strings on AdS$_3\times$ S$^3$ with Melvin deformation. The dispersion relations among various conserved charges are shown to receive finite corrections due to the deformation parameter. We further study the rotating string on AdS$_3 \times$ S$^3$ geometry with two conserved angular momenta on S$^3$ and one spin along the AdS$_3$. We show that there exists two kinds of solutions: a circular string solution and a helical string. We find out the dispersion relation among various charges and give physical interpretation of these solutions.Comment: 18 pages, 1 figure, typos fixed, minor changes, to appear in JHE

Umbilical artery Doppler indices in relation to fetal outcome in high risk pregnancy

Background: Umbilical artery Doppler indices in relation to fetal outcome in high risk pregnancy. The aim of this study was to study the umbilical artery Doppler velocimetry in predicting the fetal outcome in high risk pregnancy. This is a prospective study done over a period of 1 year in Silchar Medical College and Hospital from 1st September 2011 to 31st August 2012. 100 women with singleton pregnancy with high risk admitted in SMCH were subjected to umbilical artery Doppler along with morphology and biometry scan after fulfilling the inclusion and exclusion criteria.Methods: 100 women with high risk pregnancy were evaluated by umbilical artery velocimetry between 28 and 41 weeks of pregnancy. Outcome of pregnancy was recorded for the normal Doppler group (n = 79; 79%), the low-end diastolic flow group (n = 19; 19%) and the group with absent/reversed diastolic flow (n = 2; 2%).Results: Mothers with abnormal velocimetry had more number of caesarean sections than those with normal velocimetry. The diagnosis to delivery interval, gestational age at delivery and average birth weight were comparatively lower with higher incidence of admission to neonatal intensive care unit in foetuses with abnormal umbilical Doppler velocimetry. Sensitivity, specificity, positive and negative predictive values of Doppler for detecting abnormal fetal outcome were 43%, 83%, 33% and 88% respectively. Statistical analysis used: sensitivity, specificity and predictive values.Conclusions: Fetuses with normal flow velocimetry are at lower risk than those with abnormal velocimetry in terms of poor Apgar score and neonatal intensive care admission. The average birth weight of the neonates with abnormal Doppler studies was lower than that of neonates with normal velocimetry. Doppler velocimetry studies of umbilical artery can provide the obstetrician important information regarding fetal wellbeing to help him improve fetal outcome.

Certain subclasses of analytic function by Sălăgean q-differential operator

The theory of q-analysis has many applications in various sub-fields of mathematics and quantum physics. In the present article, we define the class Tn(α, λ; q) using the Sălăgean q-differential operator. For functions belonging to this class we obtain coefficient estimates, extreme points and integral preserving properties.Publisher's Versio

Certain subclasses of analytic function by Sǎlǎgean q-differential operator

The theory of q-analysis has many applications in various sub-fields of mathematics and quantum physics. In the present article, we define the class Tn(α, λ; q) using the Sǎlǎgean q-differential operator. For functions belonging to this class we obtain coefficient estimates, extreme points and integral preserving properties.Publisher's Versio

Misplaced Trust: Measuring the Interference of Machine Learning in Human Decision-Making

ML decision-aid systems are increasingly common on the web, but their successful integration relies on people trusting them appropriately: they should use the system to fill in gaps in their ability, but recognize signals that the system might be incorrect. We measured how people's trust in ML recommendations differs by expertise and with more system information through a task-based study of 175 adults. We used two tasks that are difficult for humans: comparing large crowd sizes and identifying similar-looking animals. Our results provide three key insights: (1) People trust incorrect ML recommendations for tasks that they perform correctly the majority of the time, even if they have high prior knowledge about ML or are given information indicating the system is not confident in its prediction; (2) Four different types of system information all increased people's trust in recommendations; and (3) Math and logic skills may be as important as ML for decision-makers working with ML recommendations.Comment: 10 page

Neumann-Rosochatius system for rotating strings in AdS3×S3×S3×S1AdS_3 \times S^3\times S^3\times S^1 with flux

Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only in $S^3\times S^1$. We further present some mathematical speculations on the rounding-off nature of the spike in the presence of non-zero angular momentum $J$ in $S^1$.Comment: 24 page