Bachground :While the main advantage of the confidence interval is that it enables more precise evaluations when the risk for the outcome of interest is related to the cluster size, the predicted confidence interval width demonstrates the degree of variability in the future data instead. Methods : We present a novel algorithm to create an intra‐cluster robust neighborhood confidence interval and width for each cluster to rank the widths from the narrowest to the widest width to determine each cluster's predicted variability and evaluate the corresponding observed values. An example was developed that assesses the finite‐sample behavior of this new method. Results : Robust neighborhood intra-cluster predicted CI width was obtained   for interpreting results  of  binary unequal sizes data. Narrow confidence intervals CI bounds suggest the results are not subjected to a high degree of random variations. Conclusions: Intra-cluster predicted robust neighborhood CI and its corresponding width is a useful instrument in binary outcome unequal cluster sizes data as a method of analysis.

Background and Objectives: This research study was conducted to determine the correlation between the clinicopathologic features and the outcome of membranous nephropathy. Materials and Methods: Data were retrospectively reviewed from all patients with a diagnosis of membranous nephropathy. Demographic, initial laboratory, and clinical findings were collected and the biopsy specimens were reviewed to classify them. To compare means, frequency, and to find correlation, student t-test, non-parametric x2 and Kendall-tau statistical tests were used respectively. A p value less than 0.05 were considered significant. Results: It was found out that during the years 1972-1996, 72 out of 2118 kidney biopsies had been diagnosed as membranous nephropathy. In this respect, male/female ratio was 2:1 (with a range of 1.5-14 years). Meanwhile, 45 out of 72 cases were idiopathic membranous nephropathy (IMN). Furthermore, 27 out of 72 had a secondary cause of the disease due to systemic lupus erythematosus (11 cases) and HBsAg positive (12 patients). The most common features in both groups were nephrotic syndrome and hematuria. In idiopathic and in chronic renal failure groups, remission occurred in 20.9% and 20.9 % of the cases respectively during an averaged  2.13 years of follow up. The statistical test Kendall-tau was used to determine the correlation between initial findings and outcome in IMN. In this regard, a significant direct correlation was found between progression to renal failure and proteinuria (p=0.009) and/or age (p=0.01) at the time of admission. For secondary membranous nephropathy, the outcomes were variable depending on the etiology. Conclusion: Proteinuria, age, and underlying etiology are the most important factors determining the renal outcome in membranous nephropathy.

This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords. Therefore, by replacing the new codewords, the binary data becomes another binary data regarding the intended goals. One of these goals is to reduce data size. It means that instead of the original codewords of each binary data, it replaced the Huffman codewords to reduce the data size. One of the features of this method is the result of positive compression for any type of binary data, that is, regardless of the size of the code table, the difference between the original data size and the data size after compression will be greater than or equal to zero. Another important and practical feature of this method is the use of symmetric codewords instead of the suggested codewords in order to create symmetry, reversibility and error resistance properties with two-way decoding.

In this article, first we define a Kripke semantics for normal modal Logic with a binary operator and we introduce a system K^2 which is sound and complete for this semantics. Then, we will introduce two translations and show that binary normal modal logic K^2, and unary normal modal logic K, i.e. modal logic with one binary operator, are very closely related by these two translations. We call a translation a faithful interpretation if provability is preserved in both directions. So, with this terminology we will show that these two translations are faithful interpretation of K into K^2 and vice versa. A logic extending K will be a set of formulas containing K closed under its rules and uniform substitution. A logic extending K^2 is similarly defined. Finally, we will prove that the classes of logics extending K and K^2 are closely related as well and there is a 1-1-correspondence between the logics extending K and extending K^2.

This review basically provided a conceptual framework for sample size calculation in epidemiologic studies with various designs and outcomes. The formula requirement of sample size was drawn based on statistical principles for both descriptive and comparative studies. The required sample size was estimated and presented graphically with different effect sizes and power of statistical test at 95% confidence level. This would help the clinicians to decide and ascertain a suitable sample size in research protocol in order to detect an effect of interest.

Elimination of redundancies in the memory representation is necessary for fast and efficient analysis of large sets of fuzzy data. In this work, we use MTBDDs as the underlying data-structure to represent fuzzy sets and binary fuzzy relations. This leads to elimination of redundancies in the representation, less computations, and faster analyses. We also extended a BDD package (BuDDy) to support MTBDDs in general and fuzzy sets and relations in particular. Representation and manipulation of MTBDD based fuzzy sets and binary fuzzy relations are described in this paper. These include design and implementation of different fuzzy operations such as max, min and max-min composition. In particular, an efficient algorithm for computing max-min composition is presented. Effectiveness of our MTBDD based implementation is shown by applying it on fuzzy connectedness and image segmentation problem. Compared to a base implementation, the running time of the MTBDD based implementation was faster (in our test cases) by a factor ranging from 2 to 27. Also, when the MTBDD based data-structure was employed, the memory needed to represent the final results was improved by a factor ranging from 37.9 to 265.5. We also describe our base implementation which is based on matrices.