Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio

The Inverse Log-Rank Test: A Versatile Procedure for Late Separating Survival Curves

Often in the planning phase of a clinical trial, a researcher will need to choose between a standard versus weighted log-rank test (LRT) for investigating right-censored survival data. While a standard LRT is optimal for analyzing evenly distributed but distinct survival events (proportional hazards), an appropriately weighted LRT test may be better suited for handling non-proportional, delayed treatment effects. The "a priori" misspecification of this alternative may result in a substantial loss of power when determining the effectiveness of an experimental drug. In this paper, the standard unweighted and inverse log-rank tests (iLRTs) are compared with the multiple weight, default Max-Combo procedure for analyzing differential late survival outcomes. Unlike combination LRTs that depend on the arbitrary selection of weights, the iLRT by definition is a single weight test and does not require implicit multiplicity correction. Empirically, both weighted methods have reasonable flexibility for assessing continuous survival curve differences from the onset of a study. However, the iLRT may be preferable for accommodating delayed separating survival curves, especially when one arm finishes first. Using standard large-sample methods, the power and sample size for the iLRT are easily estimated without resorting to complex and timely simulations.

Timelike Circular Surfaces and Singularities in Minkowski 3-Space

The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.

Introducing Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine

Structural symmetry, anti-symmetry, or asymmetry represent a foundational property that, for chemical compounds, often determines their chemical and biological activity [...]

Binomial Distributed Data Confidence Interval Calculation: Formulas, Algorithms and Examples

When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of the exact confidence interval of the sampled outcome is a mathematical challenge. This paper proposes three alternative confidence interval calculation methods that are characterized and exemplified.

An Operational DNA Strand Displacement Encryption Approach

DeoxyriboNucleic Acid (DNA) encryption is a new encryption method that appeared along with the research of DNA nanotechnology in recent years. Due to the complexity of biology in DNA nanotechnology, DNA encryption brings in an additional difficulty in deciphering and, thus, can enhance information security. As a new approach in DNA nanotechnology, DNA strand displacement has particular advantages such as being enzyme free and self-assembly. However, the existing research on DNA-strand-displacement-based encryption has mostly stayed at a theoretical or simulation stage. To this end, this paper proposes a new DNA-strand-displacement-based encryption framework. This encryption framework involves three main strategies. The first strategy was a tri-phase conversion from plaintext to DNA sequences according to a Huffman-coding-based transformation rule, which enhances the concealment of the information. The second strategy was the development of DNA strand displacement molecular modules, which produce the initial key for information encryption. The third strategy was a cyclic-shift-based operation to extend the initial key long enough, and thus increase the deciphering difficulty. The results of simulation and biological experiments demonstrated the feasibility of our scheme for encryption. The approach was further validated in terms of the key sensitivity, key space, and statistic characteristic. Our encryption framework provides a potential way to realize DNA-strand-displacement-based encryption via biological experiments and promotes the research on DNA-strand-displacement-based encryption.