System Reliability Estimation in Multicomponent Exponential-Lindley Stress-Strength Models

A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths ( ) 1 2 , ,..., k X X X are subjected to one of the r random stresses ( ) 1 2 , ,..., r Y Y Y . The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow Lindley distribution and Exponential distribution respectively. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimators

A novel medium size lactam ring analoges as antibacterial agents

A novel series of medium size (S)-3-alkyl-3,4,6,7-tetrahydro-1H-benzo[e][1,4]diazonine-2,5-dione (6a-f) analogues were synthesized from (E)-3-(2-nitrophenyl)acrylicacid (2) reacting with various amino acid esters using Di-isopropyl Carbodiimide as a coupling agent. The final cyclization is carried out by using reagent 1-Ethyl-3(3- dimethylaminopropyl) Carbodiimide Hydrochloride. The synthesized compounds have been supported by Mass, 1H-NMR and 13C-NMR. Further antibacterial studies were conducted, where some molecules are noticed with potent activity, especially molecule 6d shown highest activity which was also supported by molecular docking studies. All final molecules were docked with enzyme peptide deformylase to determine the probable binding conformation

A spin chain with non-Hermitian PT−\mathscr{PT}-symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge

We construct an exactly solvable $\mathscr{PT}-$symmetric non-Hermitian model where a spin$-\frac{1}{2}$ isotropic quantum Heisenberg spin chain is coupled to two spin$-\frac{1}{2}$ Kondo impurities at its boundaries with coupling strengths that are complex conjugates of each other. Solving the model by means of a combination of the Bethe Ansatz and density matrix renormalization group (DMRG) techniques, we show that the model exhibits three distinct boundary phases: a $\mathscr{PT}$ symmetric phase with a dissipative Kondo effect, a phase with bound modes and spontaneously broken $\mathscr{PT}$ symmetry, and a phase with an effectively unscreened spin (i.e. a free local moment). In the Kondo and the unscreened phases, the $\mathscr{PT}-$symmetry is unbroken, and hence all states have real energies, whereas in the bound mode phases, in addition to the states with real energies, there exist states with complex energy eigenvalues that appear in complex conjugate pairs, signaling spontaneous breaking of the $\mathscr{PT}-$symmetry. The exact solution is used to provide an accessible benchmark for DMRG with a non-Hermitian matrix product operator representation that demonstrates an accuracy comparable to its Hermitian limit thus showing the power of DMRG to handle non-Hermitian many body calculations.Comment: 11 pages (and 15 pages appendices) and 12+7 figure

Kondo effect in the isotropic Heisenberg spin chain

We investigate the boundary effects that arise when spin-$\frac{1}{2}$ impurities interact with the edges of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain through spin exchange interactions. We consider both cases when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the case of antiferromagnetic interaction, when the impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect. The Kondo phase is characterized by the Lorentzian density of states and dynamically generated Kondo temperature $T_K$. As the impurity coupling strength increases, $T_K$ increases until it reaches its maximum value $T_0=2\pi J$ which is the maximum energy carried by a single spinon. When the impurity coupling strength is increased further, we enter another phase, the bound mode phase, where the impurity is screened in the ground state by a single particle bound mode exponentially localized at the edge to which the impurity is coupled. We find that the impurity can be unscreened by removing the bound mode. There exists a boundary eigenstate phase transition between the Kondo and the bound-mode phases, a transition which is characterized by the change in the number of towers of the Hilbert space. The transition also manifests itself in ground state quantities like local impurity density of states and the local impurity magnetization. When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state; however, when the absolute value of the ratio of the impurity and bulk coupling strengths is greater than $\frac{4}{5}$, the impurity can be screened by adding a bound mode that costs energy greater than $T_0$. When two impurities are considered, the phases exhibited by each impurity remain unchanged in the thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.Comment: 23 pages, 7 figures; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF fil

System reliability estimation in multicomponent exponential stress-strength models

A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths (X1, X2, …, Xk) are subjected to one of the r random stresses (Xk+1, Xk+2, …, X k+r). The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow exponential distribution. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimator

System reliability estimation in multicomponent exponential stress-strength models

A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths (X1, X2, …, Xk) are subjected to one of the r random stresses (Xk+1, Xk+2, …, X k+r). The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow exponential distribution. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimator

Viscous Behaviour and Interactive Nature of Indigenous Legume Seed Galactomannas and Biodegradable Nanoparticles for Drug Delivery

Background: Galactomannans are the seed polysaccharides also known as seed gums, mostly isolated from the legume seed endosperm. Galactomannans can easily mix with xanthans by physical association, exhibits synergistic effect and form complex mixtures due to their entangle nature in deferent ratios. Polysaccharides having these properties make them versatile materials which are useful in different biomedical and food applications as additives, thickening, gelling agents, emulsifiers and stiffeners. Biopolymer-based colloidal particles have potential application in drug and gene delivery. Methods: Galactomannans extracted from indigenous legume seed endosperm from Adenanthera pavonna L and Mimosa pudica L. and investigated during 2015-2021 for different aspects i.e. viscous behaviour and interaction properties, complex formation with other polysaccharide like xanthan and preparation and physical characterisation of galactomannan-based nanoparticles obtained by covalent cross-linking with genipin. Result: The intrinsic viscosity of A. pavonna and M. pudica measured also compared with the commercial polysaccharide LBG (Locust Bean gum). Prepared small spherical shaped nanoparticles of diameters ~33 to 67 nm and negative zeta potential of ~-9.2 - 19.0 mV were obtained. We suggest that the nanoparticles form due to the covalent crosslinking effect of genipin on the residual protein fraction of both galactomannans. The biodegradable nanoparticles offer to be a potential new platform for the oral delivery of drug and nutraceuticals

Socioeconomic Deprivation and Survival After Heart Transplantation in England: An Analysis of the United Kingdom Transplant Registry.

BACKGROUND: Socioeconomic deprivation (SED) is associated with shorter survival across a range of cardiovascular and noncardiovascular diseases. The association of SED with survival after heart transplantation in England, where there is universal healthcare provision, is unknown. METHODS AND RESULTS: Long-term follow-up data were obtained for all patients in England who underwent heart transplantation between 1995 and 2014. We used the United Kingdom Index of Multiple Deprivation (UK IMD), a neighborhood level measure of SED, to estimate the relative degree of deprivation for each recipient. Cox proportional hazard models were used to examine the association between SED and overall survival and conditional survival (dependant on survival at 1 year after transplantation) during follow-up. Models were stratified by transplant center and adjusted for donor and recipient age and sex, ethnicity, serum creatinine, diabetes mellitus, and heart failure cause. A total of 2384 patients underwent heart transplantation. There were 1101 deaths during 17 040 patient-year follow-up. Median overall survival was 12.6 years, and conditional survival was 15.6 years. Comparing the most deprived with the least deprived quintile, adjusted hazard ratios for all-cause mortality were 1.27 (1.04-1.55; P=0.021) and 1.59 (1.22-2.09; P=0.001) in the overall and conditional models, respectively. Median overall survival and conditional survival were 3.4 years shorter in the most deprived quintile than in the least deprived. CONCLUSIONS: Higher SED is associated with shorter survival in heart transplant recipients in England and should be considered when comparing outcomes between centers. Future research should seek to identify modifiable mediators of this association.No direct funding was provided for the conduct of this study. JE completed part of this work as part of an academic clinical fellowship, where he spent time at the University of Cambridge, Cardiovascular Epidemiology Unit receiving training on research methods, supported by SK and EDA. The Cardiovascular Epidemiology Unit is funded by the UK Medical Research Council (G0800270), British Heart Foundation (SP/09/002), British Heart Foundation Cambridge Cardiovascular Centre of Excellence, and UK National Institute for Health Research Cambridge Biomedical Research Centre.This is the author accepted manuscript. The final version is available from American Heart Association via https://doi.org/10.1161/CIRCOUTCOMES.116.00265

Prognostic value of three iron deficiency definitions in patients with advanced heart failure

Aims: There is uncertainty about the definition of iron deficiency (ID) and the association between ID and prognosis in patients with advanced heart failure. We evaluated three definitions of ID in patients referred for heart transplantation. Methods and results: Consecutive patients assessed for heart transplantation at a single UK centre between January 2010 and May 2022 were included. ID was defined as (1) serum ferritin concentration of <100 ng/ml, or 100–299 ng/ml with transferrin saturation <20% (guideline definition), (2) serum iron concentration ≤13 μmol/L, or (3) transferrin saturation <20%. The primary outcome measure was a composite of all-cause mortality, urgent heart transplantation or need for mechanical circulatory support. Overall, 801 patients were included, and the prevalence of ID was 39–55% depending on the definition used. ID, defined by either serum iron or transferrin saturation, was an independent predictor of the primary outcome measure (hazard ratio [HR] 1.532, 95% confidence interval [CI] 1.264–1.944, and HR 1.595, 95% CI 1.323–2.033, respectively), but the same association was not seen with the guideline definition of ID (HR 1.085, 95% CI 0.8827–1.333). These findings were robust in multivariable Cox regression analysis. ID, by all definitions, was associated with lower 6-min walk distance, lower peak oxygen consumption, higher intra-cardiac filling pressures and lower cardiac output. Conclusions: Iron deficiency, when defined by serum iron concentration or transferrin saturation, was associated with increased frequency of adverse clinical outcomes in patients with advanced heart failure. The same association was not seen with guideline definition of ID