Geometric ergodicity in a weighted sobolev space

For a discrete-time Markov chain $\{X(t)\}$ evolving on $\Re^\ell$ with transition kernel $P$, natural, general conditions are developed under which the following are established: 1. The transition kernel $P$ has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space $L_\infty^{v,1}$ of functions with norm, $$\|f\|_{v,1} = \sup_{x \in \Re^\ell} \frac{1}{v(x)} \max \{|f(x)|, |\partial_1 f(x)|,\ldots,|\partial_\ell f(x)|\},$$ where $v\colon \Re^\ell \to [1,\infty)$ is a Lyapunov function and $\partial_i:=\partial/\partial x_i$. 2. The Markov chain is geometrically ergodic in $L_\infty^{v,1}$: There is a unique invariant probability measure $\pi$ and constants $B<\infty$ and $\delta>0$ such that, for each $f\in L_\infty^{v,1}$, any initial condition $X(0)=x$, and all $t\geq 0$: $$\Big| \text{E}_x[f(X(t))] - \pi(f)\Big| \le Be^{-\delta t}v(x),\quad \|\nabla \text{E}_x[f(X(t))] \|_2 \le Be^{-\delta t} v(x),$$ where $\pi(f)=\int fd\pi$. 3. For any function $f\in L_\infty^{v,1}$ there is a function $h\in L_\infty^{v,1}$ solving Poisson's equation: $$h-Ph = f-\pi(f).$$ Part of the analysis is based on an operator-theoretic treatment of the sensitivity process that appears in the theory of Lyapunov exponents

Medico-legal aspect of maternal death.

Background: With the increasing numbers legal suits against the practicing doctors now a day, it’s important to addressed sudden and unexpected death of young female during pregnancy or birth which leads to severe strain and anguish to family members. If this is not adequately resolved, healing cannot occur. It is then that the family may pursue the legal process to help obtain answers about what happened and, more importantly, why it happened to their loved one.Methods: Total 95 cases of maternal deaths which were brought for postmortem were studied during period of August 2012 to July 2014.Results: Maximum cases of deaths occurs after normal delivery 44 (46.3%) and deaths in hospital were 72 (75.8%). In 7 (7.4%) cases death was occurred during transport to medical facility. Post-partum hemorrhage remains the leading cause followed by sepsis 13 (13.7%) in direct causes of maternal deaths.Conclusions: The present study was carried out with view to determine various factors and causes of maternal deaths, utility of medicolegal autopsy and autopsy record as a useful and adjunct data source for ascertainment of maternal deaths and elucidating the emerging trends. Some special cases are discussed with the help of medicolegal knowledge, which point out fallacies while treating these cases such as proper use drugs, surgical procedures while dealing with cases of abortion and ectopic gestation, sterilization operations etc

Severe androgenetic alopecia as a maker of metabolic syndrome in male patients of androgenetic alopecia: a hospital based case control study

Background: Several previous studies have investigated the association between androgenetic alopecia (AGA) and metabolic syndrome (MS), with inconsistent results. Objectives of the study were to study the prevalence of metabolic syndrome in male patients of androgenetic alopecia and compare with control population and study the relationship of metabolic syndrome with different grades of AGA.Methods: This prospective hospital based case control study included 100 new clinically diagnosed males of androgenetic alopecia, and age and sex matched control group. Assessment for presence of various components of metabolic syndrome was done following a uniform protocol in cases and controls. AGA was classified as per Hamilton –Narwood classification, grade I to III was classified as mild –moderate and grade IV and higher as severe AGA.Results: Of the 100 male AGA patients (age range 21-50, mean 34.49), 36 had grade II AGA, 24 had grade III AGA, 20 had grade IV AGA, 15 had grade V AGA and 5 had grade VI AGA. Among AGA patients, 60 of patients had mild-moderate AGA and 40 patients had severe AGA. Metabolic syndrome was statistically significantly more common in patients with AGA compared to controls. Among patients of AGA, metabolic syndrome was statistically significantly present in severe AGA compared to mild-moderate AGA. Among the evaluated parameters, like blood pressure, fasting blood sugar, dyslipedemia, abdominal obesity, all were significantly more common in AGA patients compared to controls except abdominal obesity.Conclusions: In the present study, metabolic syndrome was found to be 4.6 times more common in patients of androgenetic alopecia as compared to controls, being statistically significant, and more common in those with severe grades. This suggests that androgenetic alopecia patients especially with severe grades are at risk of metabolic syndrome and other cardiovascular diseases

The comparative safety and effectiveness of bivalirudin versus heparin monotherapy in patients on dialysis undergoing percutaneous coronary intervention: Insights from the Blue Cross Blue Shield of Michigan cardiovascular consortium

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139064/1/ccd27001.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139064/2/ccd27001_am.pd

A study of serum lipid profile in normal pregnancy and pregnancy induced hypertensive disorders: a case-control study

Background: Pregnancy induced hypertensive disorders are one of the commonest complication of pregnancy which accounts for 12% of the maternal and perinatal mortality and morbidity. Dyslipidemias are associated with endothelial dysfunction that may result in proteinuria and hypertension which is a clinical hallmark of PIH. It affects both maternal health as well as fetal growth. Hence, this study was done to assess the role of altered lipid profile in the development of PIH.Methods: A Case Control study was conducted at the Department of Biochemistry, Kurnool Medical College and Govt General Hospital, Kurnool in collaboration with its Obstetrics Dept during the period of November 2015-2017. A total of 300 pregnant women, primigravida /multigravida with singleton pregnancy, in the age group of 18‐ 35 years with >20 weeks of gestation were included in the study. Subjects were divided into gestational hypertensives, n=39 (BP ≥140/80) and preeclamptic women, n=111 (≥140/80 and proteinuria) as cases. Age matched normotensive pregnant women, n=150 (BP 120/80) were recruited as Controls. Subjects with history of multiple pregnancies, pregnancy with congenital anomalies, chronic hypertension, diabetes mellitus, cardiac/thyroid/hepatic/renal disease, dyslipidemia were excluded. Total cholesterol, TG, HDL, LDL, VLDL were performed.Results: A comparison of these values between hypertensive and normotensive women showed a significant rise in TC, TG, LDL and VLDL. HDL-C showed a significant decrease in hypertensive women compared to normal pregnant women. LDL: HDL and TG:HDL ratios were higher in PIH group.Conclusions: The results of this study suggests an abnormal lipid metabolism, predominantly high TG concentrations and low HDL-C, which may add to the promotion of vascular dysfunction and oxidative stress seen in PIH. This association is significant in understanding the development of hypertension during pregnancy and is useful in early diagnosis and prevention of PIH

Patterns in the spectral composition of sunlight and biologically meaningful spectral photon ratios as affected by atmospheric factors

Plants rely on spectral cues present in their surroundings, generated by the constantly changing light environment, to guide their growth and reproduction. Photoreceptors mediate the capture of information by plants from the light environment over a wide range of wavelengths, but despite extensive evidence that plants respond to various light cues, only fragmentary data have been published showing patterns of diurnal, seasonal and geographical variation in the spectral composition of daylight. To illustrate patterns in spectral photon ratios, we measured time series of irradiance spectra at two distinct geographical and climatological locations, Helsinki, Finland and Gual Pahari, India. We investigated the drivers behind variation of the spectral photon ratios measured at these two locations, based on the analysis of over 400 000 recorded spectra. Differences in spectral irradiance were explained by different atmospheric factors identified through multiple regression model analysis and comparison to spectral irradiance at ground level simulated with a radiative transfer model. Local seasonal and diurnal changes in spectral photon ratios were related to solar elevation angle, atmospheric water-vapour content and total ozone column thickness and deviated from their long-term averages to an extent likely to affect plant photobiology. We suggest that future studies should investigate possible effects of varying photon ratios on terrestrial plants. Solar elevation angle especially affects the patterns of B:G and B:R ratios. Water vapour has a large effect on the R:FR photon ratio and modelled climate scenarios predict that increasing global temperatures will result in increased atmospheric water vapour. The development of proxy models, utilising available data from weather and climate models, for relevant photon ratios as a function of solar elevation angle and atmospheric factors would facilitate the interpretation of results from past, present and future field studies of plants and vegetation.Peer reviewe

A microscopic complex potential description of elastic, inelastic cross section in the Coulomb nuclear interference region in the 28Si on 28Si system

Elastic and inelastic angular distribution and excitation functions were measured for the 28Si + 28Si system in the vicinity of the Coulomb barrier. While the elastic data could be described very well by using fully microscopic complex potential, the inelastic cross sections were found to be more sensitive to small variations in the potential. In particular the Coulomb nuclear interference dip observed in the inelastic excitation functions could not be fitted satisfactorily with calculation. Inclusion of an energy dependent term of Gaussian shape to the associated matrix element with the reorientation coupling in the phenomenological calculations leads to a better fit the inelastic excitation functions. © 1998 Elsevier Science B.V

Tracking Cardiac Rehabilitation Utilization in Medicare Beneficiaries: 2017 UPDATE

PURPOSE: This study updates cardiac rehabilitation (CR) utilization data in a cohort of Medicare beneficiaries hospitalized for CR-eligible events in 2017, including stratification by select patient demographics and state of residence. METHODS: We identified Medicare fee-for-service beneficiaries who experienced a CR-eligible event and assessed their CR participation (≥1 CR sessions in 365 d), engagement, and completion (≥36 sessions) rates through September 7, 2019. Measures were assessed overall, by beneficiary characteristics and state of residence, and by primary (myocardial infarction; coronary artery bypass surgery; heart valve repair/replacement; percutaneous coronary intervention; or heart/heart-lung transplant) and secondary (angina; heart failure) qualifying event type. RESULTS: In 2017, 412 080 Medicare beneficiaries had a primary CR-eligible event and 28.6% completed ≥1 session of CR within 365 d after discharge from a qualifying event. Among beneficiaries who completed ≥1 CR session, the mean total number of sessions was 25 ± 12 and 27.6% completed ≥36 sessions. Nebraska had the highest enrollment rate (56.1%), with four other states also achieving an enrollment rate \u3e50% and 23 states falling below the overall rate for the United States. CONCLUSIONS: The absolute enrollment, engagement, and program completion rates remain low among Medicare beneficiaries, indicating that many patients did not benefit or fully benefit from a class I guideline-recommended therapy. Additional research and continued widespread adoption of successful enrollment and engagement initiatives are needed, especially among identified populations