On the Exploration of the Natural Sequence of Primes With Cellular Automata Targeting Enhanced Data Security and Privacy

Enhanced data security and privacy are one of the major concerns in today’s digital society. The role of Primes towards the enhancements of data security and privacy is undeniable. Though several prime generations were presented, yet a cost effective and an easy to implement generation of Prime sequence should always have an advantage targeting real life applications. Hence, prime sequence generation using Cellular Automata (CA) is presented in this article as CA based modelling are easy to implement at the cost of flip-flops. The main contribution of this research is to explore the natural sequence of primes (i.e., primes A000040) with a special class of group CA, at fixed boundary environment; which may potentially be used as a Prime source towards the enhancements of data security and privacy. Experimental results confirm that the first 50 members of A000040 series may be explored at automata size 8 only. Detailed investigations towards the CA configuration and its dynamics in view of the generation of prime A000040 sequence, are also presented in this article.

Prime gradient noise

Procedural noise functions are fundamental tools in computer graphics used for synthesizing virtual geometry and texture patterns. Ideally, a procedural noise function should be compact, aperiodic, parameterized, and randomly accessible. Traditional lattice noise functions such as Perlin noise, however, exhibit periodicity due to the axial correlation induced while hashing the lattice vertices to the gradients. In this paper, we introduce a parameterized lattice noise called prime gradient noise (PGN) that minimizes discernible periodicity in the noise while enhancing the algorithmic efficiency. PGN utilizes prime gradients, a set of random unit vectors constructed from subsets of prime numbers plotted in polar coordinate system. To map axial indices of lattice vertices to prime gradients, PGN employs Szudzik pairing, a bijection F: ℕ2 → ℕ. Compositions of Szudzik pairing functions are used in higher dimensions. At the core of PGN is the ability to parameterize noise generation though prime sequence offsetting which facilitates the creation of fractal noise with varying levels of heterogeneity ranging from homogeneous to hybrid multifractals. A comparative spectral analysis of the proposed noise with other noises including lattice noises show that PGN significantly reduces axial correlation and hence, periodicity in the noise texture. We demonstrate the utility of the proposed noise function with several examples in procedural modeling, parameterized pattern synthesis, and solid texturing.

mUSP: a high-accuracy map of the in situ crosstalk of ubiquitylation and SUMOylation proteome predicted via the feature enhancement approach

Reversible post-translational modification (PTM) orchestrates various biological processes by changing the properties of proteins. Since many proteins are multiply modified by PTMs, identification of PTM crosstalk site has emerged to be an intriguing topic and attracted much attention. In this study, we systematically deciphered the in situ crosstalk of ubiquitylation and SUMOylation that co-occurs on the same lysine residue. We first collected 3363 ubiquitylation-SUMOylation (UBS) crosstalk site on 1302 proteins and then investigated the prime sequence motifs, the local evolutionary degree and the distribution of structural annotations at the residue and sequence levels between the UBS crosstalk and the single modification sites. Given the properties of UBS crosstalk sites, we thus developed the mUSP classifier to predict UBS crosstalk site by integrating different types of features with two-step feature optimization by recursive feature elimination approach. By using various cross-validations, the mUSP model achieved an average area under the curve (AUC) value of 0.8416, indicating its promising accuracy and robustness. By comparison, the mUSP has significantly better performance with the improvement of 38.41 and 51.48% AUC values compared to the cross-results by the previous single predictor. The mUSP was implemented as a web server available at http://bioinfo.ncu.edu.cn/mUSP/index.html to facilitate the query of our high-accuracy UBS crosstalk results for experimental design and validation.

Mid-level Priming by Completion vs. Mosaic Solutions

We report two experiments on the role of mid-level processes in image segmentation and completion. In the primed matching task of Experiment 1, a cue→prime sequence was presented before the imperative stimulus consisting of target shapes with positive versus negative contour curvature polarity and one versus two axes of mirror symmetry. Priming shapes were included in two composite occlusion displays with the same T-junction information and different geometric features supporting a distinct balance between completion and mosaic solutions. A cue, either congruent or incongruent with targets, preceded the presentation of the composite priming display. Matching performance was affected by primes in the expected direction, while cue congruency participated only in a marginally significant three-way interaction, and prime duration had no effect. In Experiment 2, the cue→prime sequence was replaced by a fixation cross to control for the priming effect obtained in Experiment 1. The study confirmed that contour connectability and curvature polarity are effective structural factors capable of competing with symmetry in mid-level image segmentation and completion processes.

Modified Three-Dimensional Multicarrier Optical Prime Codes

We propose a mathematical model for novel three-dimensional multicarrier optical codes in terms of wavelength/time/space based on the prime sequence algorithm. The proposed model has been extensively simulated on MATLAB for prime numbers (P) to analyze the performance of code in terms of autocorrelation and cross-correlation. The simulated outcome resembles the mathematical model and gives better results over other methods available in the literature as far as autocorrelation and cross-correlation are concerned. The proposed 3D optical codes are more efficient in terms of cardinality, improved security, and providing quality of services.