Degeneracies and symmetry breaking in pseudo-Hermitian matrices

Real eigenvalues of pseudo-Hermitian matrices, such as real matrices and $\mathcal{PT-}$symmetric matrices, frequently split into complex conjugate pairs. This is accompanied by the breaking of certain symmetries of the eigenvectors and, typically, also a drastic change in the behaviour of the system. In this work, we classify the eigenspace of pseudo-Hermitian matrices and show that such symmetry breaking occurs if and only if modes of opposite kinds collide on the real axis. In particular we clarify that the degeneracy involved is not always an exceptional point. This enables a classification of the disconnected regions in parameter space where all eigenvalues are real -- which correspond, physically, to the stable phases of the system. We also discuss how our work relates to conserved quantities and to degeneracies caused by external symmetries. We illustrate our results with examples from photonics, condensed matter physics, and mechanics.Comment: 13 pages, 4 figures. Version 2 clarifies the language, expands on the examples discussed, and contains more figures. Submitted to Physical Review Research. Comments and feedback welcome

Space-time symmetry and parametric resonance in dynamic mechanical systems

Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual oscillators are well understood, identifying the conditions for parametric resonance in systems of coupled oscillators remains challenging. Here, we identify internal symmetries that arise from the real-valued and symplectic nature of classical mechanics and determine the parametric resonance conditions for periodically time-modulated mechanical metamaterials using these symmetries. Upon including external symmetries, we find additional conditions that prohibit resonances at some modulation frequencies for which parametric resonance would be expected from the internal symmetries alone. In particular, we analyze systems with space-time symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined space-time translation operator that provides more information about the system than the Floquet operator does, and use it to derive conditions for one-way amplification of traveling waves. Our results establish an exact theoretical framework based on symmetries to engineer exotic responses such as nonreciprocal transport and one-way amplification in space-time modulated mechanical systems, and can be generalized to all physical systems that obey space-time symmetry.Comment: 14 pages, 4 figure

Study of prevalence of bacterial vaginosis in preterm and term labour

Background: The objective of the study was to study the prevalence of bacterial vaginosis in women with preterm & term labour & to analyze the causal relationship of bacterial vaginosis with preterm labour.Methods: An observational study conducted on 100 patients reporting at labour room in Obstetrics & Gynaecology department of NIMS Medical College & hospital, between November 2013 to June 2014 involving 50 patients with preterm & 50 with term labour.Results: Patients who fulfilled Amsel’s criteria and patients with discharge suggestive of bacterial vaginosis were significantly more in preterm labour group as compared to term labour group. Out of 50 patients in preterm labour group, 18(36%) were suggestive of bacterial vaginosis, 32(64%) were not suggestive of bacterial vaginosis. Out of 50 patients in term labour group, 4(8%) were suggestive of bacterial vaginosis, 46(92%) were not suggestive of bacterial vaginosis.Conclusions: Bacterial vaginosis is major risk factor for preterm labour. Therefore, testing for bacterial vaginosis & prompt treatment may reduce risk of preterm labour

Comparative Analysis of Return, Net Flow and Expense Ratio of Selected Open – Ended Mutual Fund Schemes

Mutual fund industry in India has revealed a significant growth since its inception in the year 1963 even then it is far behind the developed as well as most of the emerging markets operating globally. One of the most important functions of the mutual fund industry is to mobilize the savings of the households and park their small savings in capital assets with the aim to provide them better risk adjusted return. The present study has tried to compare the return, net flow and expenses ration of the broadly classified mutual funds i.e. large cap, mid cap and small cap. Data on the selected variables have been taken for the period of 11 years from 2011 to 2021 and analyzed using one way anova. Outcomes of the study revealed that the mean return of small cap funds is highest followed by mid cap and large cap. On the basis of the outcomes this study concluded that in present there is no significant difference among the return of large cap, mid cap and small cap funds. For the variable net flow this study revealed that the average net flow of large cap funds is highest followed by small cap and mid cap funds. On the basis of the outcomes this study concluded that there is a significant difference among the net flow of large cap, mid cap and small cap funds. Average expenses of large cap funds are found lowest followed by small cap and mid cap funds. On the basis of the outcomes this study concluded that there is a significant difference among the expenses ratio of large cap, mid cap and small cap funds

Study of knowledge, attitude and practices of contraception among the married women of reproductive age group in rural area

Background: More than 40% of pregnancies worldwide are unintended leading to either an unplanned birth or unsafe abortions and maternal morbidity. India, being the most populous country, have an inherent requirement of knowing KAP of contraception among women of reproductive age to prevent unplanned pregnancies, so as to achieve optimal pregnancy outcome. Methods: A descriptive type of observational cross sectional study, involving 400 women within 18-45 year age group, were interviewed regarding KAP for various contraceptive methods. Results: Statistical analysis of data was done by using chi-square technique. Majority (82.5%) in our study had heard of contraception. In our group, 66.36% had fair knowledge, 31.21% had poor knowledge and 2.42% had good knowledge. Age, education, parity, age at marriage, association of these factors were statistically not significant. Majority (86.06%) had a negative attitude towards contraception because of rural background. Only Age (>20) was found to statistically significant for attitude towards contraception. Our study showed 43.25 % women were currently using contraceptive method, where tubal ligation was most common. Socio-demographic factors like age, education status, age at marriage were found to be statistically significant with practice or usage of contraception. Conclusions: Our study reveals that despite of fair knowledge, majority of women had negative attitude towards contraception, mainly due to rural setup, ignorance, shy nature and family pressure. Despite of fair knowledge about contraceptive methods, there usage is low. Thus, there is need for aggressive advocacy about female reproductive health with dissemination of information about family planning methods among reproductive female

The relay-converter interface influences hydrolysis of ATP by skeletal muscle myosin II

The interface between relay and converter domain of muscle myosin is critical for optimal myosin performance. Using Drosophila melanogaster indirect flight muscle S1 we performed a kinetic analysis of the effect of mutations in the converter and relay domain. Introduction of a mutation (R759E) in the converter domain inhibits the steady-state ATPase of myosin S1, whereas an additional mutation in the relay domain (N509K) is able to restore the ATPase towards wild-type values. The S1-R759E construct showed little effect on most steps of the actomyosin ATPase cycle. The exception was a 25-30% reduction in the rate constant of the hydrolysis step, the step coupled to the cross-bridge recovery stroke and involving a change in conformation at the relay/converter domain interface. Significantly the double mutant restored the hydrolysis step to values similar to the wild-type myosin. Modelling the relay/converter interface suggests a possible interaction between converter residue 759 and relay residue 509 in the actin-detached conformation, which is lost in R759E but is restored in N509K/R759E. This detailed kinetic analysis of Drosophila myosin carrying the R759E mutation shows that the interface between the relay loop and converter domain is important for fine tuning myosin kinetics, in particular ATP binding and hydrolysis