On Some Optimal Multiple Root-Finding Methods and their Dynamics

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of some of the higher-order methods in the complex plane are also given

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum

Acquisition of the Sda1-encoding bacteriophage does not enhance virulence of the serotype M1 Streptococcus pyogenes strain SF370

The resurgence of invasive disease caused by Streptococcus pyogenes (group A Streptococcus [GAS]) in the past 30 years has paralleled the emergence and global dissemination of the highly virulent M1T1 clone. The GAS M1T1 clone has diverged from the ancestral M1 serotype by horizontal acquisition of two unique bacteriophages, encoding the potent DNase Sda1/SdaD2 and the superantigen SpeA, respectively. The phage-encoded DNase promotes escape from neutrophil extracellular traps and is linked to enhanced virulence of the M1T1 clone. In this study, we successfully used in vitro lysogenic conversion to transfer the Sda1-encoding phage from the M1T1 clonal strain 5448 to the nonclonal M1 isolate SF370 and determined the impact of this horizontal gene transfer event on virulence. Although Sda1 was expressed in SF370 lysogens, no capacity of the phage-converted strain to survive human neutrophil killing, switch to a hyperinvasive covRS mutant form, or cause invasive lethal infection in a humanized plasminogen mouse model was observed. This work suggests that the hypervirulence of the M1T1 clone is due to the unique synergic effect of the M1T1 clone bacteriophage-specific virulence factor Sda1 acting in concert with the M1T1 clone-specific genetic scaffold

To study the outcome of previous one cesarean pregnancies in a rural tertiary center of Haryana, India

Background: Rising rates of caesarean section is a matter of great concern and TOLAC is an attractive alternative. Analysing outcome of previous one caesarean pregnancies will provide an insight for reducing the caesarean rates and formulating protocols and policies for TOLAC.Methods: A retrospective study of patients of previous one caesarean pregnancy was done from February 2015 to January 2016 and 3 groups were made, ERCS group, failed TOLAC group and successful TOLAC group. The rates of elective repeat caesarean, failed TOLAC, successful TOLAC, maternal complications, neonatal morbidity and mortality in all three groups were studied.Results: There were 5177 total deliveries with 488 (9.43%) previous one caesarean pregnancies. Out of 488 patients 161 (33%) underwent elective repeat caesarean and 327 (67%) underwent trial of labour. Out of 327 patients 234 (71.56%) had a successful TOLAC and 93 (28.44%) had failed TOLAC. Breech (23%) followed by foetal distress (20%) were the most common indications of previous caesarean. Commonest indication of elective repeat caesarean was short interval (33%) and that of failed TOLAC was foetal distress (38.7%) followed by failed induction (23.6%). There were 4 morbidly adherent placentas (0.82%), 1 scar rupture, 3 scar dehiscence, no maternal mortality and 10 neonatal deaths.Conclusions: Previous one caesarean section is not only a risk factor for repeat caesareans and complications like morbidly adherent placenta, uterine rupture but also a financial burden on health facilities. Encouraging the patients for trial of labour and emphasizing the usage of contraception is the need of the hour

Speckle Tracking Echocardiography for the Assessment of the Athlete's Heart: Is It Ready for Daily Practice?

PURPOSE OF REVIEW: To describe the use of speckle tracking echocardiography (STE) in the biventricular assessment of athletes' heart (AH). Can STE aid differential diagnosis during pre-participation cardiac screening (PCS) of athletes? RECENT FINDINGS: Data from recent patient, population and athlete studies suggest potential discriminatory value of STE, alongside standard echocardiographic measurements, in the early detection of clinically relevant systolic dysfunction. STE can also contribute to subsequent prognosis and risk stratification. Despite some heterogeneity in STE data in athletes, left ventricular global longitudinal strain (GLS) and right ventricular longitudinal strain (RV ɛ) indices can add to differential diagnostic protocols in PCS. STE should be used in addition to standard echocardiographic tools and be conducted by an experienced operator with significant knowledge of the AH. Other indices, including left ventricular circumferential strain and twist, may provide insight, but further research in clinical and athletic populations is warranted. This review also raises the potential role for STE measures performed during exercise as well as in serial follow-up as a method to improve diagnostic yield