Further Results on Geometric Properties of a Family of Relative Entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the R\'enyi entropy maximization rule of statistical physics.Comment: 7 pages, Prop. 5 modified, in Proceedings of the 2011 IEEE International Symposium on Information Theor

A Comparative study of Subcutaneous Suction Drainage Tube with Conventional Primary Skin Closure following Abdominal Surgeries, in case of Peritonitis

INTRODUCTION: Surgical Site Infection and delayed wound failure are reported more commonly in abdominal surgeries performed in cases of peritonitis than in other gastrointestinal surgeries. Post operative Surgical Site Infection (SSI) is a significant cause of morbidity in terms of prolonged hospital stay and increased expenses. Though pre-operative antibiotic prophylaxis and per operative thorough peritoneal lavage play a major role in preventing SSI, an effective method of closure of wound is also important. Burst abdomen following wound dehiscence in SSI is a major concern for surgeons as it can cause compromise of respiratory functions if reclosure is done, whereas, nosocomial infection can occur if the wound is left open. Subcutaneous negative suction drainage has been shown to reduce the incidence of SSI and wound dehiscence by causing drainage of the infective material and promoting wound healing. This study was done to compare the effectiveness of sub-cutaneous negative suction drainage tube and conventional abdominal wall closure in cases of peritonitis with regard to SSI, wound dehiscence, wound secondary suturing and duration of hospital stay. AIM OF THE STUDY: To compare and find out the effective method of abdominal wall closure in cases of peritonitis between subcutaneous suction drainage tube and conventional primary skin closure. STUDY DESIGN: Prospective study. MATERIALS AND METHODS: 60 patients who presented at the emergency department with acute abdominal pain and operated for the same, with features s/o peritonitis were enrolled into the study. 30 of them were managed with subcutaneous negative suction drainage tube during abdominal wall closure (Group A). 30 other patients underwent conventional method of abdominal wall closure (Group B). On table pus c/s was sent for all 60 cases. The surgical wound was observed for signs of infection. Any sero-purulent collection from the drain or any discharge from the wound was sent for c/s and the results of which were compared with the results of on table pus c/s. If wound dehiscence was noted, secondary suturing was done after the wound healed. The duration of suction drain placement and stay in the hospital were noted in all cases. STATISTICAL ANALYSIS: The results were analyzed with Chi-square test and Student t test (unpaired) and p values were calculated. A p value of less than 0.05 was considered significant. RESULTS: The incidence of SSI was significantly less in Group A (23%) than in Group B (60%). Similarly, wound dehiscence occurred in 43% of SSI cases in Group A as against 89% of SSI cases in Group B, the difference of which was statistically significant. The mean duration of hospital stay was significantly less when subcutaneous suction drain was placed (9 days). CONCLUSION: Subcutaneous suction drainage tube is an effective method of abdominal wall closure in cases of peritonitis when compared to conventional primary skin closure as it significantly reduces the incidence of SSI, wound dehiscence, wound secondary suturing and duration of hospital stay

Information Geometric Approach to Bayesian Lower Error Bounds

Information geometry describes a framework where probability densities can be viewed as differential geometry structures. This approach has shown that the geometry in the space of probability distributions that are parameterized by their covariance matrix is linked to the fundamentals concepts of estimation theory. In particular, prior work proposes a Riemannian metric - the distance between the parameterized probability distributions - that is equivalent to the Fisher Information Matrix, and helpful in obtaining the deterministic Cram\'{e}r-Rao lower bound (CRLB). Recent work in this framework has led to establishing links with several practical applications. However, classical CRLB is useful only for unbiased estimators and inaccurately predicts the mean square error in low signal-to-noise (SNR) scenarios. In this paper, we propose a general Riemannian metric that, at once, is used to obtain both Bayesian CRLB and deterministic CRLB along with their vector parameter extensions. We also extend our results to the Barankin bound, thereby enhancing their applicability to low SNR situations.Comment: 5 page