Matching Subsequences in Trees

Given two rooted, labeled trees $P$ and $T$ the tree path subsequence problem is to determine which paths in $P$ are subsequences of which paths in $T$. Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.Comment: Minor correction of typos, et

Homogenous esterification of cellulose pulp in [DBNH][OAc]

Cellulose acetate is widely used in films, filters, textiles, lacquer and cosmetic products. Herein we demonstrate the production of cellulose esters under homogeneous conditions using 1,5-diazabicyclo[4.3.0]non-5-ene acetate ([DBNH][OAc]) as solvent. The reagents have been chosen such that the system is recyclable, i.e. by-products are low boiling and easy to remove. It is demonstrated that cellulose acetate can be synthesized with different degree of substitution (DS) values, and that some commonly used acylation regents, like vinyl carboxylates react well without additional base catalyst. Low to high DS values are possible with good recovery of high purity ionic liquid (IL). A linear correlation method of two separate methods, IR and P-31 NMR, is proposed to reliably assess the DS of the products. The recyclability of the solvent is demonstrated by acetylating cellulose with isopropenyl acetate to high degree and regeneration into water. After regeneration of cellulose acetate from the IL with addition of water, the residual water was entrained using n-butanol to minimize hydrolysis of [DBNH][OAc], to allow for high recovery and high purity of the ionic liquid. Thus, an overall scheme for batch cellulose acetylation and recovery of [DBNH][OAc] from aqueous solutions is proposed.Peer reviewe

Fast Arc-Annotated Subsequence Matching in Linear Space

An arc-annotated string is a string of characters, called bases, augmented with a set of pairs, called arcs, each connecting two bases. Given arc-annotated strings $P$ and $Q$ the arc-preserving subsequence problem is to determine if $P$ can be obtained from $Q$ by deleting bases from $Q$. Whenever a base is deleted any arc with an endpoint in that base is also deleted. Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA molecules that captures both the primary and secondary structure of these. The arc-preserving subsequence problem for nested arc-annotated strings is basic primitive for investigating the function of RNA molecules. Gramm et al. [ACM Trans. Algorithms 2006] gave an algorithm for this problem using $O(nm)$ time and space, where $m$ and $n$ are the lengths of $P$ and $Q$, respectively. In this paper we present a new algorithm using $O(nm)$ time and $O(n + m)$ space, thereby matching the previous time bound while significantly reducing the space from a quadratic term to linear. This is essential to process large RNA molecules where the space is likely to be a bottleneck. To obtain our result we introduce several novel ideas which may be of independent interest for related problems on arc-annotated strings.Comment: To appear in Algoritmic

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

Clustered Single Cellulosic Fiber Dissolution Kinetics and Mechanisms through Optical Microscopy under Limited Dissolving Conditions

Herein, we describe a new method of assessing the kinetics of dissolution of single fibers by dissolution under limited dissolving conditions. The dissolution is followed by optical microscopy under limited dissolving conditions. Videos of the dissolution were processed in Image) to yield kinetics for dissolution, based on the disappearance of pixels associated with intact fibers. Data processing was performed using the Python language, utilizing available scientific libraries. The methods of processing the data include clustering of the single fiber data, identifying clusters associated with different fiber types, producing average dissolution traces and also extraction of practical parameters, such as, time taken to dissolve 25, SO, 75, 95, and 99.5% of the clustered fibers. In addition to these simple parameters, exponential fitting was also performed yielding rate constants for fiber dissolution. Fits for sample and cluster averages were variable, although demonstrating first-order kinetics for dissolution overall. To illustrate this process, two reference pulps (a bleached softwood kraft pulp and a bleached hardwood pre hydrolysis kraft pulp) and their cellulase-treated versions were analyzed. As expected, differences in the kinetics and dissolution mechanisms between these samples were observed. Our initial interpretations are presented, based on the combined mechanistic observations and single fiber dissolution kinetics for these different samples. While the dissolution mechanisms observed were similar to those published previously, the more direct link of mechanistic information with the kinetics improve our understanding of cell wall structure and pre-treatments, toward improved processability.Peer reviewe

Efficiency of hydrophobic phosphonium ionic liquids and DMSO as recyclable cellulose dissolution and regeneration media

Hydrophobic, long-chain tetraalkylphosphonium acetate salts (ionic liquids) were combined with a dipolar aprotic co-solvent, dimethylsulfoxide (DMSO), and the feasibility of these solvent systems for cellulose dissolution and regeneration was studied. A 60 : 40 w/w mixture of the ionic liquid tetraoctylphosphonium acetate ([P-8888][OAc]) and DMSO was found to dissolve up to 8 wt% cellulose, whilst trioctyl(tetradecyl) phosphonium acetate ([P-14888][OAc]) dissolved up to 3 wt% cellulose. Water (an anti-solvent for cellulose) was found to give rise to biphasic liquid-liquid systems when combined with these mixtures, yielding an upper phase rich in ionic liquid and a lower aqueous phase. The liquid-liquid equilibria of the ternary systems were experimentally determined, finding that DMSO strongly partitioned towards the aqueous phase. Thus, a process scheme involving simultaneous regeneration of cellulose and recycling of the solvent system was envisioned, and demonstrated on a large scale using [P-8888] [OAc]. A large portion of the ionic liquid (ca. 60 wt%) was directly recovered via phase separation, with a further 37 wt% being recovered from the swollen cellulose phase and residual materials, bringing recovery to 97%. XRD analysis of the recovered cellulose materials showed a loss of crystallinity and conversion from Cellulose I to Cellulose II. Non-dissolving compositions of ionic liquid and DMSO did not affect cellulose crystallinity after cellulose pulp treatment.Peer reviewe

Effects of Initial Age Structure of Managed Norway Spruce Forest Area on Net Climate Impact of Using Forest Biomass for Energy

We investigated how the initial age structure of a managed, middle boreal (62A degrees N), Norway spruce-dominated (Picea abies L. Karst.) forest area affects the net climate impact of using forest biomass for energy. The model-based analysis used a gap-type forest ecosystem model linked to a life cycle assessment (LCA) tool. The net climate impact of energy biomass refers to the difference in annual net CO2 exchange between the biosystem using forest biomass (logging residues from final felling) and the fossil (reference) system using coal. In the simulations over the 80-year period, the alternative initial age structures of the forest areas were (i) skewed to the right (dominated by young stands), (ii) normally distributed (dominated by middle-aged stands), (iii) skewed to the left (dominated by mature stands), and (iv) evenly distributed (same share of different age classes). The effects of management on net climate impacts were studied using current recommendations as a baseline with a fixed rotation period of 80 years. In alternative management scenarios, the volume of the growing stock was maintained 20% higher over the rotation compared to the baseline, and/or nitrogen fertilization was used to enhance carbon sequestration. According to the results, the initial age structure of the forest area affected largely the net climate impact of using energy biomass over time. An initially right-skewed age structure produced the highest climate benefits over the 80-year simulation period, in contrast to the left-skewed age structure. Furthermore, management that enhanced carbon sequestration increased the potential of energy biomass to replace coal, reducing CO2 emissions and enhancing climate change mitigation.Peer reviewe

Crystallinity reduction and enhancement in the chemical reactivity of cellulose by non-dissolving pre-treatment with tetrabutylphosphonium acetate

Herein, we demonstrate the activation of commercial chemical cellulose pulps towards chemical modification by a pre-treatment step with tetrabutylphosphonium acetate ([P-4444][OAc]). A heterogeneous (non-dissolving) pre-treatment was applied allowing for a significant reduction in crystallinity, without concomitant formation of the thermodynamically stable cellulose II. An increase in chemical reactivity was demonstrated using two model reactions; (1) acetylation (organic swelling conditions), where high degrees of substitution (DS) were obtained without the need for a catalyst, and (2) 4-acetamido-TEMPO oxidation (aqueous swelling conditions), where significant degrees of oxidation (DO) were obtained, beyond those for the untreated pulps. In both tests a notable improvement in cellulose reactivity was observed. Regioselectivity of acetylation was assessed using 2D NMR for one low and one high DS sample. The low DS showed a small degree of acetylation of the 6-OH, whereas, the high DS from the pre-treated sample showed mainly mixtures of triacetate and diacetates. Important mechanistic information is attained for future development of aqueous and organic-based reactions involving this ionic liquid pre-treatment.Peer reviewe