Alignment of time-course single-cell RNA-seq data with CAPITAL

Recent techniques on single-cell RNA sequencing have boosted transcriptome-wide observation of gene expression dynamics of time-course data at a single-cell scale. Typical examples of such analysis include inference of a pseudotime cell trajectory, and comparison of pseudotime trajectories between different experimental conditions will tell us how feature genes regulate a dynamic cellular process. Existing methods for comparing pseudotime trajectories, however, force users to select trajectories to be compared because they can deal only with simple linear trajectories, leading to the possibility of making a biased interpretation. Here we present CAPITAL, a method for comparing pseudotime trajectories with tree alignment whereby trajectories including branching can be compared without any knowledge of paths to be compared. Computational tests on time-series public data indicate that CAPITAL can align non-linear pseudotime trajectories and reveal gene expression dynamics.

Evidence of Absence Treated as Absence of Evidence: The Effects of Variation in the Number and Distribution of Gaps Treated as Missing Data on the Results of Standard Maximum Likelihood Analysis

We evaluated the effects of variation in the number and distribution of gaps (i.e., no base; coded as IUPAC “.” or “–”) treated as missing data (i.e., any base, coded as “?” or IUPAC “N”) in standard maximum likelihood (ML) analysis. We obtained alignments with variable numbers and arrangements of gaps by aligning seven diverse empirical datasets under different gap opening costs using MAFFT. We selected the optimal substitution model for each alignment using the corrected Akaike Information Criterion (AICc) in jModelTest2 and searched for the optimal trees for each alignment using default search parameters and the selected models in GARLI. We also employed a Monte Carlo approach to randomly insert gaps (treated as missing data) into an empirical dataset to understand more precisely the effects of their variable numbers and distributions. To compare alignments quantitatively, we used several measures to quantify the number and distribution of gaps in all alignments (e.g., alignment length, total number of gaps, total number of characters containing gaps, number of gap openings). We then used these variables to derive four indices (ranging from 0 to 1) that summarize the distribution of gaps both within and among terminals, including an index that takes into account their optimization on the tree. Our most important observation is that ML scores correlate negatively with gap opening costs, and the amount of missing data. These variables also cause unpredictable effects on tree topologies. We discuss the implications of our results for the traditional and tree-alignment approaches in ML.

Path Control of a Heat Treatment Truck Considering Driver-Vehicle Interaction

Citrus greening (Huanglongbing) has caused significant financial loss in many states of the United States and worldwide. In recent years, a heat therapy method has been investigated to prolong the production period of the diseased citrus trees after infection. One crucial step in this heat treatment process is to precisely align the truck with the diseased tree to reduce the operation time during deployment of the treatment tent. In this study, a binocular vision system is used to detect the position of the diseased tree relative to the truck, and a direct based path planning method is used to generate a nominal, optimal path for the truck to follow. A driver’s eye perception model is derived, simulating the distortion due to the human eye’s perception of objects on the computer screen, which will be used in the truck controller. A linear quadratic controller is then designed to compensate for the error coming from the eye perception mismatches and sensor and actuator noise. The studied human augmented driving control system can significantly reduce the operation time as the driver doesn’t have to constantly get out of the cab to check the truck-tree alignment. Simulation results show the effectiveness of the proposed system.

Counting, Generating, Analyzing and Sampling Tree Alignments

Pairwise ordered tree alignment are combinatorial objects that appear in important applications, such as RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis. In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees [Formula: see text] and [Formula: see text]. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal alignments.

An algebraic representation for tree alignment of RNA pseudoknotted structures

The methods proposed in the literature for RNA comparison focus mainly on pseudoknot free structures. The comparison of pseudoknotted structures is still a challenge. In this work, we propose a new algebraic representation of RNA secondary structures based on relations among hairpins in terms of nesting, crossing, and concatenation. Such algebraic representation is obtained from a defined multiple context-free grammar, which maps any kind of RNA secondary structures into extended trees, i.e., ordered trees where internal nodes are labeled with algebraic operators and leaves are labeled with loops. These extended trees permit the definition of the RNA secondary structure comparison as a tree alignment problem.

An algebraic representation for tree alignment of RNA pseudoknotted structures

The methods proposed in the literature for RNA comparison focus mainly on pseudoknot free structures. The comparison of pseudoknotted structures is still a challenge. In this work, we propose a new algebraic representation of RNA secondary structures based on relations among hairpins in terms of nesting, crossing, and concatenation. Such algebraic representation is obtained from a defined multiple context-free grammar, which maps any kind of RNA secondary structures into extended trees, i.e., ordered trees where internal nodes are labeled with algebraic operators and leaves are labeled with loops. These extended trees permit the definition of the RNA secondary structure comparison as a tree alignment problem.