Bregman and Burbea-Rao divergence for matrices

In this paper, the Bregman and Burbea-Rao divergences for matrices are investigated. Two mean-value theorems for the divergences induced by C^2-functions are derived. As application, certain Cauchy type means of the entries of the matrices are constructed. By utilizing three classes of parametrized convex functions, the exponential convexity of the divergences, thought as a function of the parameter, is proved. The monotonicity of the corresponding means of Cauchy type is shown. Power means are also considered

The n-exponential convexity for majorization inequality for functions of two variables and related results

We apply the refined method of producing n-exponential convex functions of J. Pečarić and J. Perić to extend some known results on majorization type and related inequalities

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences

Precise Computation of Energy Levels and Radiative Lifetimes in the s, p, d, and f Sequence of Hydrogen Isotope, with Natural Line Widths

Energy levels and Radiative lifetimes in Deuterium for the following: ns 2S1/2(n≥2), np2Po(1/2,3/2)(n≥2), nd 2D(3/2,5/2)(n≥3), and nf 2Fo(5/2,7/2)(n≥4) sequence have been  evaluated with uncertainties in energies caused due to uncertainty principal. Theoretical calculations performed utilizing the Weakest Bound Electron Potential Model Theory (WBEPMT). Both sets of data show quite an excellent agreement with the experimental data listed at NIST.  This theoretical computation is also a continuation of the work by Raza. S. et al. in Neutral Hydrogen. The high ‘n’ (principal quantum number) values for both sets  of data are presented very first time by utilizing WBEPMT. Keywords: Energy levels, Radiative lifetimes, Quantum defects, Weakest bound electron, Natural line width. DOI: 10.7176/JNSR/9-10-07 Publication date:May 31st 201

Inequalities for α-fractional differentiable functions

Abstract In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula

On the refinements of Jensen Mercer's inequality

In this paper we give refinements of Jensen-Mercer's inequality and its generalizations and give applications for means. We prove $n$-exponential convexity of the functions constructed from these refinements. At the end we discuss some examples

A Comparison of Dissection-method and Diathermy Tonsillectomies

Objective: To compare the dissection and diathermy methds of tonsillectomy and evaluate their advantages and disadvantages during surgery and convalescence.Methods and Setting: Patients who had tonsillectomy at Aga Khan University Hospital, between January 1994-December 1997.Results: Four year retrospective analysis was done of 200 patients who underwent tonsillectomy by either electrocautery or dissection method. One hundred and eleven underwent tonsillectomy by electrocautery and the other 79 had their tonsils removed by dissection-method and 2 had a combination of both. The average intra­operative blood loss was 10 ml with cautery and 65 ml with dissection method. The average operative time was 15.7 minutes with cautery and 26.9 minutes for dissection. We found higher amounts of blood loss and intra­operative time with dissection method than electrocautery. In comparing diathermy dissection method tonsillectomies, there was marked difference between two, in pen-operative blood loss and operative time.Conclusion: Although post-operative bleeding, pain and infection are complications of both techniques and in our study their incidence in similar in both, but intra-operative blood loss and time are two important factors,technique is a more effective technique in our set up based on which we can conclude that electrocauter

Bregman and Burbea-Rao divergence for matrices

In this paper, the Bregman and Burbea-Rao divergences for matrices are investigated. Two mean-value theorems for the divergences induced by C^2-functions are derived. As application, certain Cauchy type means of the entries of the matrices are constructed. By utilizing three classes of parametrized convex functions, the exponential convexity of the divergences, thought as a function of the parameter, is proved. The monotonicity of the corresponding means of Cauchy type is shown. Power means are also considered

Undetected common variable immune deficiency in a young adult of Pakistani descent.

Common variable immune deficiency (CVID) is a syndrome which is due to deficiency of humoral immune response resulting in increased susceptibility to infections We report a case of CVID in a 24-year-old male whopresented with a history of recurrent pneumonias

Adversarial Stacked Auto-Encoders for Fair Representation Learning

Training machine learning models with the only accuracy as a final goal may promote prejudices and discriminatory behaviors embedded in the data. One solution is to learn latent representations that fulfill specific fairness metrics. Different types of learning methods are employed to map data into the fair representational space. The main purpose is to learn a latent representation of data that scores well on a fairness metric while maintaining the usability for the downstream task. In this paper, we propose a new fair representation learning approach that leverages different levels of representation of data to tighten the fairness bounds of the learned representation. Our results show that stacking different auto-encoders and enforcing fairness at different latent spaces result in an improvement of fairness compared to other existing approaches.Comment: ICML2021 ML4data Workshop Pape