Design and testing of stand-specific bucking instructions for use on modern cut-to-length harvesters

This study addresses three important issues in tree bucking optimization in the context of cut-to-length harvesting. (1) Would the fit between the log demand and log output distributions be better if the price and/or demand matrices controlling the bucking decisions on modern cut-to-length harvesters were adjusted to the unique conditions of each individual stand? (2) In what ways can we generate stand and product specific price and demand matrices? (3) What alternatives do we have to measure the fit between the log demand and log output distributions, and what would be an ideal goodness-of-fit measure? Three iterative search systems were developed for seeking stand-specific price and demand matrix sets: (1) A fuzzy logic control system for calibrating the price matrix of one log product for one stand at a time (the stand-level one-product approach); (2) a genetic algorithm system for adjusting the price matrices of one log product in parallel for several stands (the forest-level one-product approach); and (3) a genetic algorithm system for dividing the overall demand matrix of each of the several log products into stand-specific sub-demands simultaneously for several stands and products (the forest-level multi-product approach). The stem material used for testing the performance of the stand-specific price and demand matrices against that of the reference matrices was comprised of 9 155 Norway spruce (Picea abies (L.) Karst.) sawlog stems gathered by harvesters from 15 mature spruce-dominated stands in southern Finland. The reference price and demand matrices were either direct copies or slightly modified versions of those used by two Finnish sawmilling companies. Two types of stand-specific bucking matrices were compiled for each log product. One was from the harvester-collected stem profiles and the other was from the pre-harvest inventory data. Four goodness-of-fit measures were analyzed for their appropriateness in determining the similarity between the log demand and log output distributions: (1) the apportionment degree (index), (2) the chi-square statistic, (3) Laspeyres quantity index, and (4) the price-weighted apportionment degree. The study confirmed that any improvement in the fit between the log demand and log output distributions can only be realized at the expense of log volumes produced. Stand-level pre-control of price matrices was found to be advantageous, provided the control is done with perfect stem data. Forest-level pre-control of price matrices resulted in no improvement in the cumulative apportionment degree. Cutting stands under the control of stand-specific demand matrices yielded a better total fit between the demand and output matrices at the forest level than was obtained by cutting each stand with non-stand-specific reference matrices. The theoretical and experimental analyses suggest that none of the three alternative goodness-of-fit measures clearly outperforms the traditional apportionment degree measure. Keywords: harvesting, tree bucking optimization, simulation, fuzzy control, genetic algorithms, goodness-of-fit

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.

Fuzzy Coherence: Making Sense of Continuity in Hypertext Narratives

Hypertexts are digital texts characterized by interactive hyperlinking and a fragmented textual organization. Increasingly prominent since the early 1990s, hypertexts have become a common text type both on the Internet and in a variety of other digital contexts. Although studied widely in disciplines like hypertext theory and media studies, formal linguistic approaches to hypertext continue to be relatively rare. This study examines coherence negotiation in hypertext with particularly reference to hypertext fiction. Coherence, or the quality of making sense, is a fundamental property of textness. Proceeding from the premise that coherence is a subjectively evaluated property rather than an objective quality arising directly from textual cues, the study focuses on the processes through which readers interact with hyperlinks and negotiate continuity between hypertextual fragments. The study begins with a typological discussion of textuality and an overview of the historical and technological precedents of modern hypertexts. Then, making use of text linguistic, discourse analytical, pragmatic, and narratological approaches to textual coherence, the study takes established models developed for analyzing and describing conventional texts, and examines their applicability to hypertext. Primary data derived from a collection of hyperfictions is used throughout to illustrate the mechanisms in practice. Hypertextual coherence negotiation is shown to require the ability to cognitively operate between local and global coherence by means of processing lexical cohesion, discourse topical continuities, inferences and implications, and shifting cognitive frames. The main conclusion of the study is that the style of reading required by hypertextuality fosters a new paradigm of coherence. Defined as fuzzy coherence, this new approach to textual sensemaking is predicated on an acceptance of the coherence challenges readers experience when the act of reading comes to involve repeated encounters with referentially imprecise hyperlinks and discourse topical shifts. A practical application of fuzzy coherence is shown to be in effect in the way coherence is actively manipulated in hypertext narratives.