Construction of a repetitive magic square with Ramanujan's number as its product

In this article, we build a repetitive magic square by multiplying four elements. This square is a matrix with its corresponding elements. The elements of this matrix that take different values allow us to obtain Ramanujan's number 1729 as its multiplicative magic constant. The additive magic constant of the square is the number 40. The elements of these magic constants form an arithmetic progression. An algorithm to build magic squares is also proposed.

A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square

In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the matrix's positions, and it can provide a pair of orthogonal Latin squares. Employing an n-transversal of a Latin square, we can permutate all the pixels of an image group by group for the first time, then use two Latin squares for auxiliary diffusion based on a chaotic sequence, and finally, make use of a pair of orthogonal Latin squares to perform the second scrambling. The whole encryption process is "scrambling-diffusion-scrambling". The experimental results indicated that this algorithm passed various tests and achieved a secure and fast encryption effect, which outperformed many of the latest papers. The final information entropy was very close to 8, and the correlation coefficient was approximately 0. All these tests verified the robustness and practicability of the proposed algorithm.

Association of autonomic function and brain activity with personality traits by paced breathing and su-soku practice: A three-way crossover study

OBJECTIVES

This study aimed to compare the effectiveness of paced breathing (PB) versus su-soku practice (spontaneous breathing with counting numbers) on autonomic function and brain activity and examine the associations between personality traits, brain activity, and autonomic function.

DESIGN

A three-way crossover study design.

SETTING

Thirty healthy Korean participants (15 men: 28.5 ± 4.7 years; 15 women: 27.7 ± 4.8 years) were asked to answer the Korean version of the 125-Temperament and Character Inventory (TCI). Three-way crossover design included normal PB (0.25 Hz), slow PB (0.1 Hz), and su-soku practice. Participants were randomly assigned to one of three groups (group A: su-soku/normal PB/slow PB; group B: normal PB/slow PB/su-soku; group C: slow PB/su-soku/normal PB).

MAIN OUTCOME MEASURES

The Korean version of the 125-TCI scores, electroencephalography (EEG), heart rate variability (HRV), and respiratory curve data.

RESULTS

EEG parameters between normal PB, slow PB, and su-soku showed no significant differences. High frequency and approximate entropy during normal PB and su-soku were higher than those during slow PB. Alpha band power related to well-focused alertness had strong negative correlations with the standard deviation of R-R intervals and square root of the mean of the sum of the squares of differences between adjacent R-R intervals during su-soku practice, while theta band power related to drowsiness had strong positive correlations with very low-frequency power during normal PB. Reflective and analytical individuals tended to be highly focused and alert during su-soku and normal PB, while anxious and unwilling individuals tended to focus on counting in and be drowsier during normal PB.

CONCLUSIONS

This study's findings suggest that the association between brain activity and autonomic function is affected by meditation type and personality traits.

Text messages by wireless mesh network vs voice by two-way radio in disaster simulations: A crossover randomized-controlled trial

BACKGROUND

Communication failures secondary to damaged infrastructure have caused difficulties in coordinating disaster responses. Two-way radios commonly serve as backup communication for hospitals. However, text messaging has become widely adopted in daily life and new technologies such as wireless mesh network (WMN) devices allow for text messaging independent of cellular towers, Wi-Fi networks, and electrical grids.

OBJECTIVE

To examine the accuracy of communication using text-based messaging transmitted over WMN devices (TEXT-WMN) compared to voice transmitted over two-way radios (VOICE-TWR) in disaster simulations. Secondary outcomes were patient triage accuracy, perceived workload, and device preference.

METHODS

2 × 2 Latin square crossover design: 2 simulations (each involving 15 min of simulated hospital-wide disaster communication) by 2 modalities (TEXT-WMN and VOICE-TWR). Physicians were randomized to one of two sequences: VOICE-TWR first and TEXT-WMN second; or TEXT-WMN first and VOICE-TWR second. Analyses were conducted using linear mixed effects modeling.

RESULTS

On average, communication accuracy significantly improved with TEXT-WMN compared to VOICE-TWR. Communication accuracy also significantly improved, on average, during the second simulation compared to the first. There was no significant change in triage accuracy with either TEXT-WMN or VOICE-TWR; however, triage accuracy significantly improved, on average, during the second simulation compared to the first. On average, perceived workload was significantly lower with TEXT-WMN compared to VOICE-TWR, and was also significantly lower during the second simulation compared to the first. Most participants preferred TEXT-WMN to VOICE-TWR.

CONCLUSION

TEXT-WMN technology may be more effective and less burdensome than VOICE-TWR in facilitating accurate communication during disasters.

Test equality in binary data for a 4 × 4 crossover trial under a Latin-square design

When there are four or more treatments under comparison, the use of a crossover design with a complete set of treatment-receipt sequences in binary data is of limited use because of too many treatment-receipt sequences. Thus, we may consider use of a 4 × 4 Latin square to reduce the number of treatment-receipt sequences when comparing three experimental treatments with a control treatment. Under a distribution-free random effects logistic regression model, we develop simple procedures for testing non-equality between any of the three experimental treatments and the control treatment in a crossover trial with dichotomous responses. We further derive interval estimators in closed forms for the relative effect between treatments. To evaluate the performance of these test procedures and interval estimators, we employ Monte Carlo simulation. We use the data taken from a crossover trial using a 4 × 4 Latin-square design for studying four-treatments to illustrate the use of test procedures and interval estimators developed here. Copyright © 2016 John Wiley & Sons, Ltd.

Testing equality and interval estimation of the generalized odds ratio in ordinal data under a three-period crossover design

The crossover design can be of use to save the number of patients or improve power of a parallel groups design in studying treatments to noncurable chronic diseases. We propose using the generalized odds ratio for paired sample data to measure the relative effects in ordinal data between treatments and between periods. We show that one can apply the commonly used asymptotic and exact test procedures for stratified analysis in epidemiology to test non-equality of treatments in ordinal data, as well as obtain asymptotic and exact interval estimators for the generalized odds ratio under a three-period crossover design. We further show that one can apply procedures for testing the homogeneity of the odds ratio under stratified sampling to examine whether there are treatment-by-period interactions. We use the data taken from a three-period crossover trial studying the effects of low and high doses of an analgesic versus a placebo for the relief of pain in primary dysmenorrhea to illustrate the use of these test procedures and estimators proposed here.