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

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

Pienten munuaiskasvainten ylidiagnostiikasta ylihoitoon : Voidaanko ketju katkaista?

Peer reviewe

Effects of intensified silviculture on timber production and its economic profitability in boreal Norway spruce and Scots pine stands under changing climatic conditions

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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

Renal Tumor Invasion Depth and Diameter are the Two Most Accurate Anatomical Features Regarding the Choice of Radical Versus Partial Nephrectomy

Background and Aims: To evaluate simple tumor characteristics (renal tumor diameter and parenchymal invasion depth) compared with more complex classifications, that is, Renal Tumor Invasion Index (RTII) and Preoperative Aspects and Dimensions Used for an Anatomical classification, in predicting the type of nephrectomy (radical vs partial) performed. Material and Methods: A total of 915 patients who had undergone either partial nephrectomy (n=388, 42%) or radical nephrectomy (n=527, 58%) were identified from the Helsinki University Hospital kidney tumor database between 1 January 2006 and 31 December 2014. Tumor maximum diameter and depth of invasion into the parenchyma were estimated from computed tomography or magnetic resonance imaging images and compared with Preoperative Aspects and Dimensions Used for an Anatomical and Renal Tumor Invasion Index. Logistic regression and receiver operating curves were used to compare the parameters at predicting the type of nephrectomy. Results and conclusion: All the anatomical variables of receiver operating curve/area under the curve analyses were significant predictors for the type of nephrectomy. Parenchymal invasion (area under the curve 0.91; 95% confidence interval, 0.89-0.93), RTII (area under the curve 0.91; 95% confidence interval, 0.89-0.93), and diameter (area under the curve 0.91; 95% confidence interval, 0.89-0.93) performed significantly better than Preoperative Aspects and Dimensions Used for an Anatomical classification (area under the curve 0.88; 95% confidence interval, 0.85-0.89). In multivariable analysis, invasion depth was the best predictor of nephrectomy type (percentage correct, 85.6%). Addition of one anatomic parameter into the model of non-anatomical cofactors improved the accuracy of the model significantly, but the addition of more parameters did not. Parenchymal invasion depth and tumor diameter are the most accurate anatomical features for predicting the nephrectomy type. All potential anatomical classification systems should be tested against these two simple characteristics.Peer reviewe

Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

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

Differences in branch characteristics of Scots pine (Pinus sylvestris L.) genetic entries grown at different spacing

• We studied the differences in branch characteristics along the stems of six different genetic entries of 20 year old Scots pines (Pinus sylvestris L.) grown at different spacing (current stand density range 2000–4000 trees ha−1) in central Finland. Furthermore, we studied the phenotypic correlations between yield, wood density traits and branch characteristics. All the genetic entries had Kanerva pine (plus tree S1101) as a father tree, whereas the mother tree represented Finnish plus trees from southern, central and northern Finland. • Spacing affected all yield traits, wood density and living branch characteristics such as relative average branch diameter and relative cumulative branch area (p < 0.05). As a comparison, genetic entry affected height, while origin group (southern, central and northern ones) affected most of the studied traits. Regardless of spacing, the northern origin had, on average, the largest stem diameter and highest wood density, while the central one was the tallest one. Furthermore, average branch diameter along the stem was affected by branch age, origin group and spacing, while average branch angle was affected by branch age and genetic entry (p < 0.05). • In general the average branch size could be decreased especially in lower tree canopy by denser spacing during the early phase of the rotation, but only at the expense of tree growth. Correspondingly differences between origins are mainly related to their differences in stem growth

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas