Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities

Partially ordered preferences generally lead to choices that do not abide by standard expected utility guidelines; often such preferences are revealed by imprecision in probability values. We investigate five criteria for strategy selection in decision trees with imprecision in probabilities: “extensive” Γ-maximin and Γ-maximax, interval dominance, maximality and E-admissibility. We present algorithms that generate strategies for all these criteria; our main contribution is an algorithm for Eadmissibility that runs over admissible strategies rather than over sets of probability distributions.

Compact Routing Messages in Self-Healing Trees

Existing compact routing schemes, e.g., Thorup and Zwick [SPAA 2001] and Chechik [PODC 2013], often have no means to tolerate failures, once the system has been setup and started. This paper presents, to our knowledge, the first self-healing compact routing scheme. Besides, our schemes are developed for low memory nodes, i.e., nodes need only O(log2 n) memory, and are thus, compact schemes.
We introduce two algorithms of independent interest: The first is CompactFT, a novel compact version (using only O(log n) local memory) of the self-healing algorithm Forgiving Tree of Hayes et al. [PODC 2008]. The second algorithm (CompactFTZ) combines CompactFT with Thorup-Zwick’s treebased compact routing scheme [SPAA 2001] to produce a fully compact self-healing routing scheme. In the self-healing model, the adversary deletes nodes one at a time with the affected nodes self-healing locally by adding few edges. CompactFT recovers from each attack in only O(1) time and ∆ messages, with only +3 degree increase and O(log∆) graph diameter increase, over any sequence of deletions (∆ is the initial maximum degree).
Additionally, CompactFTZ guarantees delivery of a packet sent from sender s as long as the receiver has not been deleted, with only an additional O(y log ∆) latency, where y is the number of nodes that have been deleted on the path between s and t. If t has been deleted, s gets informed and the packet removed from the network.

SHORT-TERM EFFECTS OF SALINITY ON SOME PHYSIOLOGICAL PARAMETERS OF YOUNG OLIVE TREES OF ARBEQUINA, COBRANÇOSA AND GALEGA VARIETIES

SHORT-TERM EFFECTS OF SALINITY ON SOME PHYSIOLOGICAL PARAMETERS OF YOUNG OLIVE TREES OF ARBEQUINA, COBRANÇOSA AND GALEGA VARIETIES Ana Elisa Rato1,4, Renato Coelho1, Margarida Vaz1, Teresa Carola2, Dália Barbosa2, Nádia Silva1, José dos Santos2, Lourenço Machado2, João Godinho2, Luzia Ruas2, Margarida Barradas2, Hernani Pereira2, Sara Porfírio4 1 ICAAM, Universidade de Évora, Apartado 94, 7002-554 Évora, Portugal 2 Master students, Universidade de Évora, Apartado 94, 7002-554 Évora, Portugal 3 Ph.D. student, Universidade de Évora, Apartado 94, 7002-554 Évora, Portugal 4 aerato@uevora.pt Due to the desertification in some regions, the interest in plant’s tolerance to salinity has been increasing, as this response is determining for plant survival in stress conditions. This work reports the investigation of tolerance to salt in two year-old olive trees (Olea europaea L.) of three varieties, Arbequina, Cobrançosa and Galega vulgar. Plants were grown in 10 L plastic pots containing approximately 9 Kg of a sandy granitic soil, on a greenhouse. For 3 months (from the beginning of February to the end of April 2012), they were subjected to three levels of salinity in the irrigation water, 0 mM, 80 mM and 200 mM NaCl (6 plants per salinity level in a total of 18 plants of each variety),. Stomatal conductance (gs) and relative leaf chlorophyll content were assessed on each plant in February, March and April. Mid-day leaf water potential () and soil salinity were measured at the end of the experiment (April). On average, concerning all treatments and dates of determination, stomatal conductance of Arbequina and Galega vulgar was quite similar, around 40 mmol m-2 s-1, but Cobrançosa had a value of gs 36% higher, almost 50% higher (61 mmol m-2 s-1) when compared with the controls (0 mM salt) of the other two varieties. In percentage of controls, there was little difference in gs between varieties and between salinities during February and March. In contrast, in April, after about 90 days of exposure to salt, there was a clear decrease in gs with salt irrigation, proportional to salt concentration. Compared with controls, plants irrigated with 200 mM salt showed around 80% (Arbequina) or 85% (Cobrançosa and Galega vulgar) decrease in gs. Chlorophyll content of leaves showed less than 5% difference between varieties on the average of all treatments and dates of determination. During the course of this experiment, the salinity levels used did not show any relevant effect on chlorophyll content. Overall, at the end of the experimental period (April), leaf water potential () at midday was significantly higher in Cobrançosa (-1,4 MPa) than in Galega vulgar (-1,7 MPa) or Arbequina (-1,8 MPa), and salt decreased  of control plants (-1,25 MPa) by an average 30% (with 80 mM) and 65% (with 200 mM). At the end of the experiment, salinity in the soil irrigated with 0 mM, 80 mM or 200 mM NaCl was, on average of all varieties, 0,2 mS, 1,0 mS or 2,0 mS, respectively. Soil salinity was quite similar in Arbequina and Galega vulgar but about 35% lower in the pots of Cobrançosa, on average of all salt-irrigation levels. Plants of Cobrançosa had higher stomatal conductance, however they showed higher water potential and lower salinity in the soil. These apparently contradictory results seem to suggest that Cobrançosa responds to salt differently from the other two varieties. This issue needs further investigation.

Response to salinity in young olive trees of three Iberian varieties

Soil salinization is a problem in the Mediterranean region. This paper reports a research on the response to salt in two year-old olive trees (Olea europaea L.) of three Iberian varieties: Arbequina, Cobrançosa and Galega Vulgar. Plants were grown in plastic pots containing approximately 9 Kg of a sandy granitic soil, on a greenhouse at the University of Évora since February 2010. The experiment went from February to April 2012. As a rule, plants were watered every other day alternating salt solution (0 mM, 80 mM or 200 mM NaCl) or tap water. After three months irrigation with the different NaCl solutions, soil electric conductivity and soil water content were significantly higher on salt-irrigated pots. Salt also decreased significantly stomatal conductance (gs) and mid-day leaf water potential (), Cobrançosa having in general higher gs and but lower SLA than the two other varieties. Chlorophyll content of leaves was not affected by salt after this three months exposure to NaCl but was significantly higher on Arbequina and lower on Cobrançosa. In general, hyperspectral reflectance indexes did not show significant correlations with salt irrigation, except for the Photochemical Reflectance Index (PRI) which was clearly lower on plants of all three varieties irrigated with salt. Interestingly, Cobrançosa showed frequently vegetation indexes different from the other two varieties.

Micropropagation in elite corck oak trees: a tool for suber production improvement?

Dada a extrema importância económica e ambiental que o montado de sobro tem em Portugal, e dado o declínio deste devido a várias razões (e.g. doença, idade das plantas) é premente desenvolver estratégias de preservação de sobreiros elite e optimizar técnicas para a propagação destes genótipos. No primeiro Capítulo expõe-se uma breve introdução sobre o montado actual e as técnicas actuais de regeneração/propagação do sobreiro. Descreve-se ainda as principais técnicas de preservação e avaliação de estabilidade genética referidas na literatura para sobreiro e outras lenhosas. No Capítulo II é apresentado um estudo de melhoramento das condições actuais de maturação de embriões somáticos de sobreiro com vista a aperfeiçoar o processo de conversão em plantas. Neste capítulo é apresentado um protocolo melhorado em relação ao actual que permite um desenvolvimento dos embriões somáticos dum modo semelhante aos embriões zigóticos em termos de substâncias de reserva. O Capítulo III mostra um estudo efectuado com o objectivo principal de avaliar estabilidade genética durante todo o processo de embriogénese somática. Neste capítulo são apresentados resultados duma análise feita por RAPD em fases distintas da embriogénese somática de sobreiro. Neste estudo mostra-se que não existem diferenças significativas entre plantas de campo, embriões somáticos e plantas regeneradas. No Capítulo VI, pretende-se complementar o estudo anterior. Neste Capítulo descreve-se a dinâmica do ciclo celular durante as primeiras fases de embriogénese somática na presença de reguladores de crescimento. Este trabalho permitiu concluir a importância dos reguladores de crescimento na indução e perceber o peso do factor genótipo durante o processo. Considerando os resultados anteriores, a necessidade de um processo eficiente de preservação de genótipos elite torna-se fundamental. No Capítulo V descreve-se um protocolo de criopreservação eficiente sem recursos a substâncias tóxicas. Nesta secção é ainda feita uma análise de variabilidade genética após criopreservação através de FCM, AFLP e SSR. Todos os resultados obtidos anteriormente são postos a prova no Capítulo VI onde se faz uma monitorização extensiva de 10 genótipos elite, tendo em conta a sua capacidade de produção de cortiça, através do processo de embriogénese somática. Durante esta secção são utilizados os protocolos desenvolvidos anteriormente e avaliados na sua eficiência. Neste capítulo é descrita a integração de vários segmentos deste estudo num só protocolo eficiente de regeneração e preservação de sobreiros através de embriogénese somática. Finalmente, no Capítulo VI são apresentadas as conclusões da presente Tese de Doutoramento, com especial incidência para linhas de investigação futuras a serem tomadas. Discute-se a importância deste novo protocolo na optimização da produção da cortiça e traçam-se possíveis aplicações alternativas.

Mathematics as Grammar

Tésis de Doctorado en Filosofía, Universidad de Indiana, Bloomington, 2000

Effect of nitrogen and potassium fertilisation on vegetative growth and flowering of mature carob trees (Ceratonia siliqua): variations in leaf area index and water use indices

This work aimed to assess how potassium (K) and nitrogen (N) fertilisation may affect the use of precipitation in terms of vegetative and flowering response of 15-year-old carob trees during a 3-year experiment. A field trial was conducted in 1997, 1998 and 1999 in Algarve (Southern Portugal) in a calcareous soil. Four fertilisation treatments were tested: no fertiliser (control); 0.8 kg N/tree (N treatment); 1 kg K 2 O/tree (K treatment) and 0.8 kg N/tree plus 1 kg K 2 O/tree (NK treatment). No irrigation was applied during the experimental period. Branch length increments were measured every month throughout the growing season and inflorescence number was registered once per year. There was a strong seasonal effect on vegetative growth, since low levels of precipitation (115 mm) during October 1998–March 1999 suppressed the increment in branch length. N supplied to the trees (N and NK treatments) tended to increase water use indices in terms of vegetative growth. No response to K alone was observed in trees fertilised only with K. The number of inflorescences increased throughout the experimental period, particularly for N and NK treatments, and a reduction of the precipitation amount during April, May and June, may also enhance flowering. This knowledge could be important when making decisions concerning fertilisation under dry conditions. The results reported here indicate that tree growth (expressed as the branch growth) and flower production under dry-farming conditions, may be achieved by applying 0.8 kg of N (as ammonium nitrate) per tree during the growing season. However, N uptake and use depends on soil water availability.

Changes in the Pollen Seasons of the Early Flowering Trees Alnus spp. and Corylus spp. in Worcester United Kingdom 1996-2005

Previous work on Betula spp. (birch) in the UK and at five sites in Europe has shown that pollen seasons for this taxon have tended to become earlier by about 5–10 days per decade in most regions investigated over the last 30 years. This pattern has been linked to the trend to warmer winters and springs in recent years. However, little work has been done to investigate the changes in the pollen seasons for the early flowering trees. Several of these, such as Alnus spp. and Corylus spp., have allergens, which cross-react with those of Betula spp., and so have a priming effect on allergic people. This paper investigates pollen seasons for Alnus spp. and Corylus spp. for the years 1996–2005 at Worcester, in the West Midlands, United Kingdom. Pollen data for daily average counts were collected using a Burkard volumetric trap sited on the exposed roof of a three-storey building. The climate is western maritime. Meteorological data for daily temperatures (maximum and minimum) and rainfall were obtained from the local monitoring sites. The local area up to approximately 10 km surrounding the site is mostly level terrain with some undulating hills and valleys. The local vegetation is mixed farmland and deciduous woodland. The pollen seasons for the two taxa investigated are typically late December or early January to late March. Various ways of defining the start and end of the pollen seasons were considered for these taxa, but the most useful was the 1% method whereby the season is deemed to have started when 1% of the total catch is achieved and to have ended when 99% is reached. The cumulative catches (in grains/m3) for Alnus spp. varied from 698 (2001) to 3,467 (2004). For Corylus spp., they varied from 65 (2001) to 4,933 (2004). The start dates for Alnus spp. showed 39 days difference in the 10 years (earliest 2000 day 21, latest 1996 day 60). The end dates differed by 26 days and the length of season differed by 15 days. The last 4 years in the set had notably higher cumulative counts than the first 2, but there was no trend towards earlier starts. For Corylus spp. start days also differed by 39 days (earliest 1999 day 5, latest 1996 day 44). The end date differed by 35 days and length of season by 26 days. Cumulative counts and lengths of season showed a distinct pattern of alternative high (long) and low (short) years. There is some evidence of a synchronous pattern for Alnus spp.. These patterns show some significant correlations with temperature and rainfall through the autumn, winter and early spring, and some relationships with growth degree 4s and chill units, but the series is too short to discern trends. The analysis has provided insight to the variation in the seasons for these early flowering trees and will form a basis for future work on building predictive models for these taxa.

Are the Birch Trees in Southern England a Source of Betula Pollen for North London?

Birch pollen is highly allergenic. Knowledge of daily variations, atmospheric transport and source areas of birch pollen is important for exposure studies and for warnings to the public, especially for large cities such as London. Our results show that broad-leaved forests with high birch tree densities are located to the south and west of London. Bi-hourly Betula pollen concentrations for all the days included in the study, and for all available days with high birch pollen counts (daily average birch pollen counts >80 grains/m3), show that, on average, there is a peak between 1400 hours and 1600 hours. Back-trajectory analysis showed that, on days with high birch pollen counts (n=60), 80% of air masses arriving at the time of peak diurnal birch pollen count approached North London from the south in a 180 degree arc from due east to due west. Detailed investigations of three Betula pollen episodes, with distinctly different diurnal patterns compared to the mean daily cycle, were used to illustrate how night-time maxima (2200–0400 hours) in Betula pollen counts could be the result of transport from distant sources or long transport times caused by slow moving air masses. We conclude that the Betula pollen recorded in North London could originate from sources found to the west and south of the city and not just trees within London itself. Possible sources outside the city include Continental Europe and the Betula trees within the broad-leaved forests of Southern England.

A Community-Level, Mesoscale Analysis of Fish Assemblage Structure in Shoreline Habitats of a Large River Using Multivariate Regression Trees.

The mesoscale (100–102 m) of river habitats has been identified as the scale that simultaneously offers insights into ecological structure and falls within the practical bounds of river management. Mesoscale habitat (mesohabitat) classifications for relatively large rivers, however, are underdeveloped compared with those produced for smaller streams. Approaches to habitat modelling have traditionally focused on individual species or proceeded on a species-by-species basis. This is particularly problematic in larger rivers where the effects of biological interactions are more complex and intense. Community-level approaches can rapidly model many species simultaneously, thereby integrating the effects of biological interactions while providing information on the relative importance of environmental variables in structuring the community. One such community-level approach, multivariate regression trees, was applied in order to determine the relative influences of abiotic factors on fish assemblages within shoreline mesohabitats of San Pedro River, Chile, and to define reference communities prior to the planned construction of a hydroelectric power plant. Flow depth, bank materials and the availability of riparian and instream cover, including woody debris, were the main variables driving differences between the assemblages. Species strongly indicative of distinctive mesohabitat types included the endemic Galaxias platei. Among other outcomes, the results provide information on the impact of non-native salmonids on river-dwelling Galaxias platei, suggesting a degree of habitat segregation between these taxa based on flow depth. The results support the use of the mesohabitat concept in large, relatively pristine river systems, and they represent a basis for assessing the impact of any future hydroelectric power plant construction and operation. By combing community classifications with simple sets of environmental rules, the multivariate regression trees produced can be used to predict the community structure of any mesohabitat along the reach.

Curriculum and beyond: Mathematics support for first year life science students

The move into higher education is a real challenge for students from all educational backgrounds, with the adaptation to a new curriculum and style of learning and teaching posing a daunting task. A series of exercises were planned to boost the impact of the mathematics support for level four students and was focussed around a core module for all students. The intention was to develop greater confidence in tackling mathematical problems in all levels of ability and to provide more structured transition period in the first semester of level 4. Over a two-year period the teaching team for Biochemistry and Molecular Biology provided a series of structured formative tutorials and “interactive” online problems. Video solutions to all formative problems were made available, in order that students were able to engage with the problems at any time and were not disadvantaged if they could not attend. The formative problems were specifically set to dovetail into a practical report in which the mathematical skills developed were specifically assessed. Students overwhelmingly agreed that the structured formative activities had broadened their understanding of the subject and that more such activities would help. Furthermore, it is interesting to note that the package of changes undertaken resulted in a significant increase in the overall module mark over the two years of development.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.