The Ranking Problem of Alternatives as a Cooperative Game

This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to construct a characteristic function via the filled ballot paper profile of voters. The Shapley value serves as the ranking method. The winner is the candidate having the maximum Shapley value. And finally, we explore the properties of the designed ranking procedure

Minimal Envy and Popular Matchings

We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects -- minimal envy matching. A matching is fair from social perspective if it is supported by majority against any other matching -- popular matching. Surprisingly, the two perspectives give the same outcome: when a popular matching exists it is equivalent to a minimal envy matching. We show the equivalence between global and local popularity: a matching is popular if and only if there does not exist a group of size up to 3 agents that decides to exchange their objects by majority, keeping the remaining matching fixed. We algorithmically show that an arbitrary matching is path-connected to a popular matching where along the path groups of up to 3 agents exchange their objects by majority. A market where random groups exchange objects by majority converges to a popular matching given such matching exists. When popular matching might not exist we define most popular matching as a matching that is popular among the largest subset of agents. We show that each minimal envy matching is a most popular matching and propose a polynomial-time algorithm to find them

Development of thermodynamic methods for quantification and understanding of non-covalent interactions in molecular and ionic systems

Dispersion and non-covalent interactions are often responsible for the intramolecular stabilization of flexible or strained molecules, so taking these forces into account is a crucial contribution to rationalizing the unexpected stabilities of such molecules. To quantify non-covalent interactions in such well-defined molecular and ionic systems, we have developed and validated three thermodynamic methods based on the “experimental” enthalpy of vaporization and enthalpy of formation as well as based on the “theoretical” DFT-calculated energy.Dispersion und nicht-kovalente Wechselwirkungen sind oft für die intramolekulare Stabilisierung flexibler oder gespannter Moleküle verantwortlich, daher ist die Berücksichtigung dieser Kräfte ein wichtiger Beitrag zur Erklärung der unerwarteten Stabilitäten solcher Moleküle. Um nicht-kovalente Wechselwirkungen in solchen gut-definierten molekularen und ionischen Systemen zu quantifizieren, haben wir drei thermodynamische Methoden entwickelt und validiert, die auf der „experimentellen“ Verdampfungs- und Bildungsenthalpien sowie auf der „theoretischen“ DFT-berechneten Energie basieren

Fair and consistent prize allocation in competitions

Given the final ranking of a competition, how should the total prize endowment be allocated among the competitors? We study consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we axiomatically characterize two families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the Equal Division rule and the Winner-Takes-All rule. Specific characterizations of rules and subfamilies are directly obtained.Comment: 34 page

Tectonics and volcanisms of Mars

Televised images of Mars transmitted from interplanetary stations are used to develop a theory of the structure and development of the planet. Crater chronology, the structure of planetary bodies in the Earth group, and a comparison of the Earth planetary bodies are among the factors included

Identification of mechanisms defining resistance and susceptibility of Camellia plants to necrotrophic petal blight disease : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Plant Biology at Massey University, Manawatū, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesAll Figures are re-used with publishers' permission.Species in the genus Camellia, which includes the tea crops, oil-producers and valuable ornamental plants, have economic and cultural significance for many countries. The fungus Ciborinia camelliae causes petal blight disease of Camellia plants, which has a short initial asymptomatic phase and results in rapid necrosis and fall of blooms. Ciborinia camelliae is a necrotrophic pathogen of the family Sclerotiniaceae, which also includes two broad-host range necrotrophic pathogens, Botrytis cinerea and Sclerotinia sclerotiorum. Previously it was shown that some Camellia plants, such as Camellia lutchuensis, are naturally resistant to petal blight. In order to find molecular mechanisms underpinning this resistance, a genome-wide analysis of gene expression in C. lutchuensis petals was conducted. The analysis revealed a fast modulation of host transcriptional activity in response to C. camelliae ascospores. Interaction network analysis of fungus-responsive genes showed that petal blight resistance includes increased expression of important plant defence pathways, such as WRKY33-MPK3, phenylpropanoid and jasmonate biosynthesis. A much-delayed activation of the same pathways was observed in the susceptible Camellia cultivar, Camellia ‘Nicky Crisp’ (Camellia japonica x Camellia pitardii var. pitardii), suggesting that failure to activate early defence enables C. camelliae to invade and cause tissue necrosis. Early artificial induction of defence pathways using methyl jasmonate reduced the rate of petal blight in susceptible ‘Nicky Crisp’ plants, further verifying the role of a rapid defence activation in petal-blight resistance. Overall, transcriptomic and functional analysis of the Camellia spp.- C. camelliae interaction demonstrated that the same plant defence pathways contribute to both resistance and susceptibility against this necrotrophic pathogen, depending on the timing of their activation. To further understand the molecular mechanisms of petal blight resistance, the role of the phenylpropanoid pathway, identified as a key feature in the transcriptome study above, was investigated in more detail. This pathway produces various metabolites, including phenolic acids, aldehydes, and alcohols, which have numerous physiological functions and also participate in the production of flavonoids and lignin. Resistant C. lutchuensis was shown to rapidly activate the expression of core phenylpropanoid genes after treatment with C. camelliae ascospores. LC-MS-based quantification of phenylpropanoid compounds demonstrated that within the first 6 h of the infection, resistant plants had already accumulated coumaric, ferulic and sinapic acids, while at 24 hpi, concentrations of coumaraldehyde, sinapaldehyde, and caffeyalcohol were significantly increased. Thus, I further hypothesized that the compounds produced by the phenylpropanoid pathway may have fungistatic activity. Indeed, all tested phenylpropanoids inhibited the growth of C. camelliae in agar plates with different efficacy. Moreover, the application of phenylpropanoid compounds, including ferulic and coumaric acids, fully prevented the formation of petal blight lesions on susceptible Camellia ‘Nicky Crisp’ petals. Taken together, it can be concluded that the phenylpropanoid pathway may contribute to the early defence against the petal blight via the rapid production of fungistatic compounds. Ultimately, these compounds could be used to develop natural antifungal sprays to protect susceptible Camellia flowers. The analysis of the C. camelliae secretome using LC-MS/MS detection of proteins showed that the pathogen produces a large number of carbohydrate-active enzymes in liquid culture and plant petals. Injection of these proteins induced necrosis not only in susceptible Camellia petals but also in petals of the resistant species and leaves of non-host Nicotiana benthamiana. It was proposed that these enzymes can contribute to the virulence of the pathogen by inducing cell death and facilitating necrosis propagation. Thus, the early defence responses of resistant Camellia plants may possibly stop the development of C. camelliae before it starts releasing carbohydrate-active enzymes during the necrotrophic step of the infection. Overall, the results of this research further expand our understanding of plant- necrotroph interactions, suggesting that the timing of plant immune responses may be a crucial factor defining the outcome of the necrotrophic infection

On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions

By Birman and Skvortsov it is known that if \Omegasf is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain H^2(\Omegasf)\cap H^1_0(\Omegasf) is a closed symmetric operator with deficiency indices $(n,n)$. Here we provide a Kre\u\i n-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on \Omegasf, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions.Comment: Slightly revised version. Accepted for publication in Journal of Functional Analysi

MECHANISMS OF DESTRUCTION AND SYNTHESIS OF LIQUID MEDIA, USED IN THE FOOD INDUSTRY UNDER NON-EQUILIBRIUM CONDITIONS

The formation of food liquid medium structures containing at least 70 % of disperse particles with high dispersiveness has been considered. The possible formation mechanisms of food liquid medium structure when slow (hydrodynamic) and quick (acoustic) processes create favorable conditions for cavitation have been studied. The possibility to control these processes for initiation of mechanical and kinetic reactions that change the structure of the medium has been demonstrated. The invert syrup has been selected as the study object. The change in the invert syrup structure before and after such cavitation treatment has been recorded with the use of metallographic microscope Nikon Eclipse MA100. The decrease in disperse phase sizes from 2–3 µm to 0.1–0.4 µm along with establishing the high uniformity of component distribution as compared to the syrup without cavitation process treatment has been detected. The formation of food liquid medium structures containing at least 70 % of disperse particles with high dispersiveness has been considered. The possible formation mechanisms of food liquid medium structure when slow (hydrodynamic) and quick (acoustic) processes create favorable conditions for cavitation have been studied. The possibility to control these processes for initiation of mechanical and kinetic reactions that change the structure of the medium has been demonstrated. The invert syrup has been selected as the study object. The change in the invert syrup structure before and after such cavitation treatment has been recorded with the use of metallographic microscope Nikon Eclipse MA100. The decrease in disperse phase sizes from 2–3 µm to 0.1–0.4 µm along with establishing the high uniformity of component distribution as compared to the syrup without cavitation process treatment has been detected.

Small domain estimation of census coverage: A case study in Bayesian analysis of complex survey data

Many countries conduct a full census survey to report official population statistics. As no census survey ever achieves 100 per cent response rate, a post-enumeration survey (PES) is usually conducted and analysed to assess census coverage and produce official population estimates by geographic area and demographic attributes. Considering the usually small size of PES, direct estimation at the desired level of disaggregation is not feasible. Design-based estimation with sampling weight adjustment is a commonly used method but is difficult to implement when survey non-response patterns cannot be fully documented and population benchmarks are not available. We overcome these limitations with a fully model-based Bayesian approach applied to the New Zealand PES. Although theory for the Bayesian treatment of complex surveys has been described, published applications of individual level Bayesian models for complex survey data remain scarce. We provide such an application through a case study of the 2018 census and PES surveys. We implement a multilevel model that accounts for the complex design of PES. We then illustrate how mixed posterior predictive checking and cross-validation can assist with model building and model selection. Finally, we discuss potential methodological improvements to the model and potential solutions to mitigate dependence between the two surveys.Comment: 35 pages, 5 figures This is an author version of a paper accepted for publication in the Journal of Official Statistics. Once published by the Journal of Official Statistics use the Journal citation. This version includes supplementary material and corrected version of Figure