The transcriptomic datasets of the plant model organism Arabidopsis thaliana grown in the International Space Station provided by GeneLab have been mined to isolate the impact of spaceflight microgravity on gene expressions related to root growth. A set of computational tools is used to identify the hub genes that respond differently in spaceflight with controlled lighting compared to on the ground. These computational tools based on graph-theoretic approaches are used to infer gene regulatory networks from the transcriptomic datasets. The three main algorithms used for network analyses are Least Absolute Shrinkage and Selection Operator (LASSO), Pearson correlation, and the Hyperlink-Induced Topic Search (HITS) algorithm. Graph-based spectral analyses reveal distinct properties of the spaceflight microgravity networks for the Wassilewskija (WS), Columbia (Col)-0, and mutant phytochromeD (phyD) ecotypes. The set of hub genes that are significantly altered in spaceflight microgravity are mainly involved in cell wall synthesis, protein transport, response to auxin, stress responses, and catabolic processes. Network analysis highlights five important root growth-regulating hub genes that have the highest outdegree distribution in spaceflight microgravity networks. These concerned genes coding for proteins are identified from the Gene Regulatory Networks (GRNs) corresponding to spaceflight total light environment. Furthermore, network analysis uncovers genes that encode nucleotide-diphospho-sugar interconversion enzymes that have higher transcriptional regulation in spaceflight microgravity and are involved in cell wall biosynthesis.

Spaceflight microgravity affects normal plant growth in several ways. The transcriptional dataset of the plant model organism Arabidopsis thaliana grown in the international space station is mined using graph-theoretic network analysis approaches to identify significant gene transcriptions in microgravity essential for the plant’s survival and growth in altered environments. The photosynthesis process is critical for the survival of the plants in spaceflight under different environmentally stressful conditions such as lower levels of gravity, lesser oxygen availability, low atmospheric pressure, and the presence of cosmic radiation. Lasso regression method is used for gene regulatory network inferencing from gene expressions of four different ecotypes of Arabidopsis in spaceflight microgravity related to the photosynthetic process. The individual behavior of hub-genes and stress response genes in the photosynthetic process and their impact on the whole network is analyzed. Logistic regression on centrality measures computed from the networks, including average shortest path, betweenness centrality, closeness centrality, and eccentricity, and the HITS algorithm is used to rank genes and identify interactor or target genes from the networks. Through the hub and authority gene interactions, several biological processes associated with photosynthesis and carbon fixation genes are identified. The altered conditions in spaceflight have made all the ecotypes of Arabidopsis sensitive to dehydration-and-salt stress. The oxidative and heat-shock stress-response genes regulate the photosynthesis genes that are involved in the oxidation-reduction process in spaceflight microgravity, enabling the plant to adapt successfully to the spaceflight environment.

An almost perfect nonlinear (APN) function $f:\mathbb{F}_{2^n}\rightarrow\mathbb{F}_{2^n}$ (necessarily polynomial) is called exceptional APN if it is APN on infinitely many extensions of $\mathbb{F}_{2^n}$. Aubry, McGuire and Rodier conjectured that the only exceptional APN functions are the Gold and the Kasami-Welch monomial functions. They established that a polynomial function of odd degree is not exceptional APN provided the degree is not a Gold number $(2^k+1)$ or a Kasami-Welch number $(2^{2k}-2^k+1)$. When the degree of the polynomial function is a Gold number or a Kasami-Welch number, several partial results have been obtained by several authors including us. In this article we address these exceptions. We almost prove the exceptional APN conjecture in the Gold degree case when $\deg{(h(x))}$ is odd. We also show exactly when the corresponding multivariate polynomial $φ(x, y, z)$ is absolutely irreducible. Also, there is only one result known when $f(x)=x^{2^{k}+1} + h(x)$, and $\deg(h(x))$ is even. Here, we extend this result as well, thus making progress in this case that seems more difficult.