The structure of Norway spruce (Picea abies [L.] Karst.) stems in relation to wood properties of sawn timber

An important challenge in forest industry is to get the appropriate raw material out from the forests to the wood processing industry. Growth and stem reconstruction simulators are therefore increasingly integrated in industrial conversion simulators, for linking the properties of wooden products to the three-dimensional structure of stems and their growing conditions. Static simulators predict the wood properties from stem dimensions at the end of a growth simulation period, whereas in dynamic approaches, the structural components, e.g. branches, are incremented along with the growth processes. The dynamic approach can be applied to stem reconstruction by predicting the three-dimensional stem structure from external tree variables (i.e. age, height) as a result of growth to the current state. In this study, a dynamic growth simulator, PipeQual, and a stem reconstruction simulator, RetroSTEM, are adapted to Norway spruce (Picea abies [L.] Karst.) to predict the three-dimensional structure of stems (tapers, branchiness, wood basic density) over time such that both simulators can be integrated in a sawing simulator. The parameterisation of the PipeQual and RetroSTEM simulators for Norway spruce relied on the theoretically based description of tree structure developing in the growth process and following certain conservative structural regularities while allowing for plasticity in the crown development. The crown expressed both regularity and plasticity in its development, as the vertical foliage density peaked regularly at about 5 m from the stem apex, varying below that with tree age and dominance position (Study I). Conservative stem structure was characterized in terms of (1) the pipe ratios between foliage mass and branch and stem cross-sectional areas at crown base, (2) the allometric relationship between foliage mass and crown length, (3) mean branch length relative to crown length and (4) form coefficients in branches and stem (Study II). The pipe ratio between branch and stem cross-sectional area at crown base, and mean branch length relative to the crown length may differ in trees before and after canopy closure, but the variation should be further analysed in stands of different ages and densities with varying site fertilities and climates. The predictions of the PipeQual and RetroSTEM simulators were evaluated by comparing the simulated values to measured ones (Study III, IV). Both simulators predicted stem taper and branch diameter at the individual tree level with a small bias. RetroSTEM predictions of wood density were accurate. For focusing on even more accurate predictions of stem diameters and branchiness along the stem, both simulators should be further improved by revising the following aspects in the simulators: the relationship between foliage and stem sapwood area in the upper stem, the error source in branch sizes, the crown base development and the height growth models in RetroSTEM. In Study V, the RetroSTEM simulator was integrated in the InnoSIM sawing simulator, and according to the pilot simulations, this turned out to be an efficient tool for readily producing stand scale information about stem sizes and structure when approximating the available assortments of wood products.

Kidney Induction: control by Notch, Wnt and GDNF/Ret signalling

The permanent mammalian kidney (metanephros) develops as a result of complex reciprocal tissue interactions between a ureteric epithelium and the renal mesenchyme. The overall goal of the research in this thesis was to gain data that will eventually help in elucidating the formation of congenital renal malformations. The experiments in my thesis aimed to reveal the mechanisms by which Notch, Wnt and GDNF/Ret signalling pathways regulate the development of functional kidney. The function of Notch pathway was studied by a transgenic mouse model, where it was shown that overactivation of Notch signalling disturbs kidney development and alters the expression of Gdnf and Ret/GFRa1. This indicates that Notch signalling interplays with GDNF/Ret in the regulation of the primary ureteric budding and its subsequent branching. The data also suggested that strict spatio-temporal regulation of these two pathways is required for determination of ureteric tip-identity, which appeared to be crucial for the branch formation. The function of Wnt signalling in the ureteric morphogenesis was studied by in vivo and in vitro methods to show that a canonical pathway is required for ureteric branching. Stabilisation and deletion of the canonical pathway mediator, b-catenin specifically in the ureteric epithelium result in renal aplasia/hypodysplasia. These defects originate from severe blockage of ureteric branching due to the disrupted Ret signalling. Consequently, ureteric tip specific markers are lost and ureteric stalk identity is expanded throughout the whole epithelium. Thus, the data demonstrates that the Wnt/b-catenin pathway plays an essential role in the patterning and branching of the ureteric epithelium. A novel in vitro method was generated and utilised in nephron induction studies to reveal the mechanisms through which nephrogenesis is induced. Transient GSK3 inhibition results in stabilisation of b-catenin in the isolated renal mesenchyme, which efficiently triggers nephron formation. Also genetic stabilisation of b-catenin specifically in the mesenchyme results in spontaneous nephrogenesis. The results show that activation of the canonical Wnt pathway is sufficient to initiate nephrogenesis, and suggest that this pathway mediates the nephron induction in murine kidney mesenchymes. Taken together, this thesis demonstrates Notch and Wnt signalling pathways as novel regulators of ureteric branching morphogenesis, and that activation of the canonical Wnt pathway is sufficient for nephron induction. The studies also indicate that the Notch and Wnt pathways cross-talk with GDNF/Ret signalling in the patterning of ureteric epithelium.

Regulation of strawberry growth and development

Strawberries (Fragaria sp.) are adapted to diverse environmental conditions from the tropics to about 70ºN, so different responses to environmental conditions can be found. Most genotypes of garden strawberry (F. x ananassa Duch.) and woodland strawberry (F. vesca L.) are short-day (SD) plants that are induced to flowering by photoperiods under a critical limit, but also various photoperiod x temperature interactions can be found. In addition, continuously flowering everbearing (EB) genotypes are found. In addition to flowering, axillary bud differentiation in strawberry is regulated by photoperiod. In SD conditions, axillary buds differentiate to rosette-like structures called "branch crowns", whereas in long-day conditions (LD) they form runners, branches with 2 long internodes followed by a daughter plant (leaf rosette). The number of crown branches determines the yield of the plant, since inflorescences are formed from the apical meristems of the crown. Although axillary bud differentiation is an important developmental process in strawberries, its environmental and hormonal regulation has not been characterized in detail. Moreover, the genetic mechanisms underlying axillary bud differentiation and regulation of flowering time in these species are almost completely unresolved. These topics have been studied in this thesis in order to enhance strawberry research, cultivation and breeding. The results showed that 8-12 SD cycles suppressed runner initiation from the axillary buds of the garden strawberry cv. Korona with the concomitant induction of crown branching, and 3 weeks of SD was sufficient for the induction of flowering in the main crown. Furthermore, a second SD treatment given a few weeks after the first SD period can be used to induce flowering in the primary branch crowns and to induce the formation of secondary branches. Thus, artificial SD treatments effectively stimulate crown branching, providing one means for the increase of cropping (yield) potential in strawberry. It was also shown by growth regulation applications, quantitave hormone analysis and gene expression analysis that gibberellin (GA) is one of the key signals involved in the photoperiod control of shoot differentiation. The results indicate that photoperiod controls GA activity specifically in axillary buds, thereby determining bud fate. It was further shown that chemical control of GA biosynthesis by prohexadione-calcium can be utilized to prevent excessive runner formation and induce crown branching in strawberry fields. Moreover, ProCa increased berry yield up to 50%, showing that it is an easier and more applicable alternative to artificial SD treatments for controlling strawberry crown development and yield. Finally, flowering gene pathways in Fragaria were explored by searching for homologs of 118 Arabidopsis thaliana flowering-time genes. In total, 66 gene homologs were identified, and they distributed to all known flowering pathways, suggesting the presence of these pathways also in strawberry. Expression analysis of selected genes revealed that the mRNA of putative floral identity gene APETALA1 accumulated in the shoot apex of the EB genotype after the induction of flowering, whereas it was absent in vegetative SD genotype, indicating the usefulness of this gene product as the marker of floral initiation. The present data enables the further exploration of strawberry flowering pathways with genetic transformation, gene mapping and transcriptomics methods.

DNA-based detection and characterisation of strictly anaerobic beer-spoilage bacteria

Megasphaera cerevisiae, Pectinatus cerevisiiphilus, Pectinatus frisingensis, Selenomonas lacticifex, Zymophilus paucivorans and Zymophilus raffinosivorans are strictly anaerobic Gram-stain-negative bacteria that are able to spoil beer by producing off-flavours and turbidity. They have only been isolated from the beer production chain. The species are phylogenetically affiliated to the Sporomusa sub-branch in the class "Clostridia". Routine cultivation methods for detection of strictly anaerobic bacteria in breweries are time-consuming and do not allow species identification. The main aim of this study was to utilise DNA-based techniques in order to improve detection and identification of the Sporomusa sub-branch beer-spoilage bacteria and to increase understanding of their biodiversity, evolution and natural sources. Practical PCR-based assays were developed for monitoring of M. cerevisiae, Pectinatus species and the group of Sporomusa sub-branch beer spoilers throughout the beer production process. The developed assays reliably differentiated the target bacteria from other brewery-related microbes. The contaminant detection in process samples (10 1,000 cfu/ml) could be accomplished in 2 8 h. Low levels of viable cells in finished beer (≤10 cfu/100 ml) were usually detected after 1 3 d culture enrichment. Time saving compared to cultivation methods was up to 6 d. Based on a polyphasic approach, this study revealed the existence of three new anaerobic spoilage species in the beer production chain, i.e. Megasphaera paucivorans, Megasphaera sueciensis and Pectinatus haikarae. The description of these species enabled establishment of phenotypic and DNA-based methods for their detection and identification. The 16S rRNA gene based phylogenetic analysis of the Sporomusa sub-branch showed that the genus Selenomonas originates from several ancestors and will require reclassification. Moreover, Z. paucivorans and Z. raffinosivorans were found to be in fact members of the genus Propionispira. This relationship implies that they were carried to breweries along with plant material. The brewery-related Megasphaera species formed a distinct sub-group that did not include any sequences from other sources, suggesting that M. cerevisiae, M. paucivorans and M. sueciensis may be uniquely adapted to the brewery ecosystem. M. cerevisiae was also shown to exhibit remarkable resistance against many brewery-related stress conditions. This may partly explain why it is a brewery contaminant. This study showed that DNA-based techniques provide useful tools for obtaining more rapid and specific information about the presence and identity of the strictly anaerobic spoilage bacteria in the beer production chain than is possible using cultivation methods. This should ensure financial benefits to the industry and better product quality to customers. In addition, DNA-based analyses provided new insight into the biodiversity as well as natural sources and relations of the Sporomusa sub-branch bacteria. The data can be exploited for taxonomic classification of these bacteria and for surveillance and control of contaminations.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Regional Integration and the State : The Changing Nature of Sovereignty in Southern Africa and Europe

The study explores the role of the state in regional integration processes. The question is approached through theoretical discussion and two case-studies - SADC (Southern African Development Community) and the EU. The main research question of the study is, what are the possibilities and problems of the integration process in Southern Africa and how do they differ from the possibilities and problems of the integration process in Europe. The undelrying question of the study is why do states decide to participate in an integration process where they have to limit their sovereignty. Review of the theoretical discussion of the integration studies shows that the integration process is affected by several factors on different levels of the international system. But the state plays a central role in integration processes - integration processes are inititated and carried on by the participatig states. The European integration process shows that the interests of the state can change over time. At the beginning of the integration process, the objective was to strengthen participating states. Later EU member states have decided that it is in their interest to deepen the process even if it has meant limitation of their sovereignty. The determinant factor has been that the member states have considered it to be in their interst to deepen the process. In Southern Africa the integration process is only at the beginning. SADC aims to establish a free trade area by 2008. The biggest challenge is how to implement the integration process so that it benefits all member states in a region that is economically dominated by South Africa. In practice this can be achieved through establishment of corrective mechanisms, which ensure equitable distribution of benefits. This would require deeper integration and South Africa to adapt responsibility towards its regional partners. African integration processes in general have not been as successful as for example the EU. African states have been reluctant to limit their sovereignty in favour of regional organisations.This can be explained by the differences between European and African states. The EU member states have been democracies while African states have been characterised by concentration of power in the executive branch. Furthermore the political systems in Africa have been characterised by vertical clientelist reltionships. As a result it has not been in the interest of the political elite to limit the state sovereignty in favour of regional organisations. In recent years SADC has been relatively succesful in its integration process and reforms, but a lot remains to be done before the implementation of the free trade area can be succesful. The institutional structure and treaties of SADC differ from the structures of the EU. Member states are the main actors of the integration processes. Their differences are reflected in the process and produce different kinds of integration in different parts of the world.

Seismic Tomography and Earthquake Mechanism Beneath the Central Fennoscandian Shield

The aim of this thesis was to study the seismic tomography structure of the earth s crust together with earthquake distribution and mechanism beneath the central Fennoscandian Shield, mainly in southern and central Finland. The earthquake foci and some fault plane solutions are correlated with 3-D images of the velocity tomography. The results are discussed in relation to the stress field of the Shield and with other geophysical, e.g. geomagnetic, gravimetric, tectonic, and anisotropy studies of the Shield. The earthquake data of the Fennoscandian Shield has been extracted from the Nordic earthquake parameter data base which was founded at the time of inception of the earthquake catalogue for northern Europe. Eight earlier earthquake source mechanisms are included in a pilot study on creating a novel technique for calculating an earthquake fault plane solution. Altogether, eleven source mechanisms of shallow, weak earthquakes are related in the 3-D tomography model to trace stresses of the crust in southern and central Finland. The earthquakes in the eastern part of the Fennoscandian Shield represent low-active, intraplate seismicity. Earthquake mechanisms with NW-SE oriented horizontal compression confirm that the dominant stress field originates from the ridge-push force in the North Atlantic Ocean. Earthquakes accumulate in coastal areas, in intersections of tectonic lineaments, in main fault zones or are bordered by fault lines. The majority of Fennoscandian earthquakes concentrate on the south-western Shield in southern Norway and Sweden. Onwards, epicentres spread via the ridge of the Shield along the west-coast of the Gulf of Bothnia northwards along the Tornio River - Finnmark fault system to the Barents Sea, and branch out north-eastwards via the Kuusamo region to the White Sea Kola Peninsula faults. The local seismic tomographic method was applied to find the terrane distribution within the central parts of the Shield the Svecofennian Orogen. From 300 local explosions a total of 19765 crustal Pg- and Sg-wave arrival times were inverted to create independent 3-D Vp and Vs tomographic models, from which the Vp/Vs ratio was calculated. The 3-D structure of the crust is presented as a P-wave and for the first time as an S-wave velocity model, and also as a Vp/Vs-ratio model of the SVEKALAPKO area that covers 700x800 km2 in southern and central Finland. Also, some P-wave Moho-reflection data was interpolated to image the relief of the crust-mantle boundary (i.e. Moho). In the tomography model, the seismic velocities vary smoothly. The lateral variations are larger for Vp (dVp =0.7 km/s) than for Vs (dVs =0.4 km/s). The Vp/Vs ratio varies spatially more distinctly than P- and S-wave velocities, usually from 1.70 to 1.74 in the upper crust and from 1.72 to 1.78 in the lower crust. Schist belts and their continuations at depth are associated with lower velocities and lower Vp/Vs ratios than in the granitoid areas. The tomography modelling suggests that the Svecofennian Orogen was accreted from crustal blocks ranging in size from 100x100 km2 to 200x200 km2 in cross-sectional area. The intervening sedimentary belts have ca. 0.2 km/s lower P- and S-wave velocities and ca. 0.04 lower Vp/Vs ratios. Thus, the tomographic model supports the concept that the thick Svecofennian crust was accreted from several crustal terranes, some hidden, and that the crust was later modified by intra- and underplating. In conclusion, as a novel approach the earthquake focal mechanism and focal depth distribution is discussed in relation to the 3-D tomography model. The schist belts and the transformation zones between the high- and low-velocity anomaly blocks are characterized by deeper earthquakes than the granitoid areas where shallow events dominate. Although only a few focal mechanisms were solved for southern Finland, there is a trend towards strike-slip and oblique strike-slip movements inside schist areas. The normal dip-slip type earthquakes are typical in the seismically active Kuusamo district in the NE edge of the SVEKALAPKO area, where the Archean crust is ca. 15-20 km thinner than the Proterozoic Svecofennian crust. Two near vertical dip-slip mechanism earthquakes occurred in the NE-SW junction between the Central Finland Granitoid Complex and the Vyborg rapakivi batholith, where high Vp/Vs-ratio deep-set intrusion splits the southern Finland schist belt into two parts in the tomography model.

Does relationship marketing improve customer relationship satisfaction and loyalty?

Purpose - This study investigates the relationship marketing (RM) strategy of a retail bank and examines whether - after its implementation - customer relationships were strengthened through perceived improvements in the banking relationship and consequent loyalty towards the bank. Design/methodology/approach - A survey was conducted on two profitability segments, of which the more profitable segment had been directly exposed to a customer oriented RM strategy, whereas the less profitable segment had been subjected to more sales oriented marketing communications. Findings - No significant differences were found between the segments on customers’ evaluations of the service relationship or their loyalty toward the bank. Furthermore regression analysis revealed that relationship satisfaction was less important as a determinant of loyalty in the more profitable segment. Research limitations/implications - This study was conducted as a case study of one specific branch of a bank group in Finland, which limits the external validity of its results. It was not possible to ascertain if, or to what extent, customers of the more profitable segment had received the intended RM treatment. Other limitations are also discussed. Practical implications - Customer orientation is desirable within retail banking and more studies are needed on the differential drivers of loyalty across customer profitability segments. By identifying the aspects of a banking relationship that are more highly valued among more profitable customers than among less profitable customers, bank managers would be able to more effectively devise appropriate strategies for different segments. Originality/value - The study contributes to the RM literature and marketing of financial services by providing empirical evidence of the effects of RM activities on customer relationship perceptions in different profitability segments.

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept taken from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical coherence and consistency . This investigation provides a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. This research analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Looking forward in this direction, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature: proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. Using quantitative qualitative methods, evidence is presented to justify a parallel study of different modalities of musical self-similarity. For this purpose, original arguments by Benoît B. Mandelbrot are revised, alongside a systematic critique of the literature on the subject. Furthermore, connecting Charles S. Peirce s synechism with Mandelbrot s fractality is one of the main developments of the present study. This study provides elements for explaining Bolognesi s (1983) conjecture, that states that the most primitive, intuitive and basic musical device is self-reference, extending its functions and operations to self-similar surfaces. In this sense, this research suggests that, with various modalities of self-similarity, synecdochic intersemiosis acts as system of systems in coordination with greater or lesser development of structural consistency, and with a greater or lesser contextual dependence.

Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.