A counterexample to Beder's conjectures about Hadamard matrices

In this note we provide a counterexample which resolves conjectures about Hadamard matrices made in this journal. Beder [1998. Conjectures about Hadamard matrices. Journal of Statistical Planning and Inference 72, 7–14] conjectured that if H$\mathit{H}$ is a maximal m×n$m\times n$ row-Hadamard matrix then m is a multiple of 4; and that if n   is a power of 2 then every row-Hadamard matrix can be extended to a Hadamard matrix. Using binary integer programming we obtain a maximal 13×32$13\times 32$ row-Hadamard matrix, which disproves both conjectures. Additionally for n being a multiple of 4 up to 64, we tabulate values of m   for which we have found a maximal row-Hadamard matrix. Based on the tabulated results we conjecture that a m×n$m\times n$ row-Hadamard matrix with m?n-7$m?n-7$ can be extended to a Hadamard matrix.     

Visceral adiposity index is associated with premature ejaculation inversely: a cross-sectional study

Objective: Visceral adiposity index (VAI) is a novel indicator for the assessment of visceral obesity. In this study, we aimed to evaluate the relationship between VAI and premature ejaculation (PE).

Materials and method: A total of 300 men were included in the study. Hundred and fifty men with PE and 150 men without PE (control). All men were evaluated for PE by premature ejaculation diagnostic tool (PEDT). VAI levels were calculated using body mass index (BMI), high density lipoprotein and triglyceride (TG) levels.

Results: Mean age of the study groups was 34.3?±?5.2 (30–60) years and the mean age of the controls were 35.9?±?5.3 (30–60) years. The men with PE had lower BMI, TG levels, waist circumference (WC) and higher high-density lipoprotein-cholesterol (HDL-C) levels. Mean VAI level was 4.13?±?0.7 in study group and 5.72?±?1.6 in control group, respectively. VAI levels were statistically higher in men without PE (p?Discussion: Our cross-sectional study demonstrated a negative correlation between VAI and PE. VAI is superior index for the evaluation and calculation the relationship between obesity and PE.     

Optimal Pricing Strategies for Capacity Leasing Based on Time and Volume Usage in Telecommunication Networks

In this study, we examined optimal pricing strategies for “pay‐per‐time,” “pay‐per‐volume,” and “pay‐per‐both‐time‐and‐volume” based leasing of data networks in a monopoly environment. Conventionally, network capacity distribution includes short‐/long‐term bandwidth and/or usage time leasing. When customers choose connection‐time–based pricing, their rational behavior is to fully utilize the bandwidth capacity within a fixed time period, which may cause the network to burst (or overload). Conversely, when customers choose volume‐based strategies their rational behavior is to send only the minimum bytes necessary (even for time‐fixed tasks for real time applications), causing the quality of the task to decrease, which in turn creates an opportunity cost for the provider. Choosing a pay‐per time and volume hybridized pricing scheme allows customers to take advantage of both pricing strategies while lessening the disadvantages of each, because consumers generally have both time‐ and size‐fixed tasks such as batch data transactions. One of the key contributions of this study is to show that pay‐per both time and volume pricing is a viable and often preferable alternative to the offerings based on only time or volume, and that judicious use of such a pricing policy is profitable to the network provider.     

Increased visceral adiposity index associated with sexual dysfunction in men

Objective: Visceral adipose index (VAI) is a novel parameter for the evaluation of visceral obesity. As we know that obesity is a risk factor for erectile dysfunction (ED). So, in this study, we compared the VAI levels between the men with ED and without ED.

Materials and method: A total of 177 men were included in the study. Ninety-five men with ED and 82 men without ED (control). All men were evaluated for ED by Index of Erectile Function-5 items (IIEF-5). VAI levels were calculated using body mass index, high density lipoprotein and tryglyceride levels.

Results: Mean age was 53.5 (38–69) in men who have ED and 53.1 (34–69) in control. The men with ED had higher body mass index (BMI), triglyceride (TG) levels, higher waist circumference (WC) and lower high-density lipoprotein-cholesterol (HDL-C) levels. Mean VAI level was 5.18?±?2.50 in study group and 3.47?±?1.76 in control goup, respectively. VAI levels were statistically higher in men with ED (p?Discussion: The simplicity of WC and BMI measurement and TG and HDL assessment, make VAI an easily applicable index for the evaluation of visceral fat dysfunction. VAI can be useful index for the evaluation and calculation of erectile dysfunction risk.     

Visceral adiposity index is associated with benign prostatic enlargement in non-diabetic patients: a cross-sectional study

Objective: To evaluate the association between visceral adiposity index (VAI) - a novel indicator for the assessment of visceral adipose tissue and prostate enlargement in non diabetic patients.

Material and methods: Four hundred patients who were admitted to the Urology clinic between January and December 2014 with complaints of BPH(benign prostatic hyperplasia )/LUTS(male lower urinary tract symptoms)were enrolled in this cross-sectional study. Patients were divided into two groups according to their prostate volume and international prostate symptom score (IPSS) value. They were compared in terms of age, body mass index (BMI), VAI, prostate volume, PSA, post micturional residual volume (PMRV), uroflowmetry Q max value, triglyceride (TG), high density lipoprotein-cholesterol (HDL-C) and fasting blood sugar (FBS).

Results: Although univariate analyses reveal that age, BMI, waist circumference (WC), FBS, TG, HDL-C level and TG/HDL ratio were correlated with prostate volume, only age [1.125 OR (1.088–1.164), p?=?.00001], BMI [1.119 OR (1.040–1.204), p?=?.003], TG [1.043 OR (1.016–1.071), p?=?.002], HDL-C [0.923 OR (0.860–0.990), p?=?.025] and VAI [1.194 OR (1.110–1.305), p?=?.011] were statistically significant in multivariate analysis. A positive correlation was found between VAI value and prostate volume in the Spearman correlation test (r?=?0.29, p?=?.00001). The calculated area under the curve (AUC) for prostate volumes of 30, 40 and 50?ml were 0.680 (0.621–0.738), 0.625 (0.570–0.681) and 0.590 (0.528–0.652), respectively.

Conclusion: Our study revealed a positive correlation between VAI and prostate volume. Our results are needed to be tested with well-designed randomized prospective cohort studies.     

Modified spline regression based on randomly right-censored data: A comparative study

ABSTRACT

In this paper, we propose modified spline estimators for nonparametric regression models with right-censored data, especially when the censored response observations are converted to synthetic data. Efficient implementation of these estimators depends on the set of knot points and an appropriate smoothing parameter. We use three algorithms, the default selection method (DSM), myopic algorithm (MA), and full search algorithm (FSA), to select the optimum set of knots in a penalized spline method based on a smoothing parameter, which is chosen based on different criteria, including the improved version of the Akaike information criterion (AICc), generalized cross validation (GCV), restricted maximum likelihood (REML), and Bayesian information criterion (BIC). We also consider the smoothing spline (SS), which uses all the data points as knots. The main goal of this study is to compare the performance of the algorithm and criteria combinations in the suggested penalized spline fits under censored data. A Monte Carlo simulation study is performed and a real data example is presented to illustrate the ideas in the paper. The results confirm that the FSA slightly outperforms the other methods, especially for high censoring levels.     

Improved WLP and GWP lower bounds based on exact integer programming

By using exact integer programming (IP) (integer programming in infinite precision) bounds on the word-length patterns (WLPs) and generalized word-length patterns (GWPs) for fractional factorial designs are improved. In the literature, bounds on WLPs are formulated as linear programming (LP) problems. Although the solutions to such problems must be integral, the optimization is performed without the integrality constraints. Two examples of this approach are bounds on the number of words of length four for resolution IV regular designs, and a lower bound for the GWP of two-level orthogonal arrays. We reformulate these optimization problems as IP problems with additional valid constraints in the literature and improve the bounds in many cases. We compare the improved bound to the enumeration results in the literature to find many cases for which our bounds are achieved. By using the constraints in our integer programs we prove that f(16λ,2,4)?9$f(16\lambda ,2,4)?9$ if λ$\lambda$ is odd where f(2^tλ,2,t)$f(2^t\lambda ,2,t)$ is the maximum n   for which an OA(N,n,2,t)$\mathrm{OA}(N,n,2,t)$ exists. We also present a theorem for constructing GMA OA(N,N/2-u,2,3)$\mathrm{OA}(N,N/2-u,2,3)$ for u=1,…,5$u=1,\dots ,5$.