In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In the second part of this dissertation, we introduce an alternative approach to approximately implement QPE with arbitrary constantprecision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev’s original approach. For approximating the eigenphase precise to the nth bit, Kitaev’s original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev’s approach. iii The other problem we investigate relates to approximating the Tutte polynomial. We show that the problem of approximately evaluating the Tutte polynomial of triangular graphs at the points (q, 1/q) of the Tutte plane is BQP-complete for (most) roots of unity q. We also consider circular graphs and show that the problem of approximately evaluating the Tutte polynomial of these graphs at the point (e 2πi/5 ,e−2πi/5 ) is DQC1-complete and at points (q k , 1 + 1−q−k (q 1/2−q−1/2) 2 ) for some integer k is in BQP. To show that these problems can be solved by a quantum computer, we rely on the relation of the Tutte polynomial of a planar G graph with the Jones and HOMFLY polynomial of the alternating link D(G) given by the medial graph of G. In the case of our graphs the corresponding links are equal to the plat and trace closures of braids. It is known how to evaluate the Jones and HOMFLY polynomial for closures of braids. To establish the hardness results, we use the property that the images of the generators of the braid group under the irreducible Jones-Wenzl representations of the Hecke algebra have finite order. We show that for each braid b we can efficiently construct a braid ˜b such that the evaluation of the Jones and HOMFLY polynomials of their closures at a fixed root of unity leads to the same value and that the closures of ˜b are alternating links. The final part of the dissertation focuses on finding the structure of a black-box module or algebra. Suppose we are given black-box access to a finite module M or algebra over a finite ring R, and a list of generators for M and R. We show how to find a linear basis and structure constants for M in quantum poly(log |M|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for rings. We then show that iv our algorithm is a useful primitive allowing quantum computers to determine the structure of a finite associative algebra as a direct sum of simple algebras. Moreover, it solves a wide variety of problems regarding finite modules and rings. Although our quantum algorithm is based on Abelian Fourier transforms, it solves problems regarding the multiplicative structure of modules and algebras, which need not be commutative. Examples include finding the intersection and quotient of two modules, finding the additive and multiplicative identities in a module, computing the order of an module, solving linear equations over modules, deciding whether an ideal is maximal, finding annihilators, and testing the injectivity and surjectivity of ring homomorphisms. These problems appear to be exponentially hard classically.

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23684号 / 理博第4774号 / 新制||理||1684(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 小野 薫, 教授 玉川 安騎男, 教授 望月 拓郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Thesis (Ph.D. Agriculture (Plant Production)) -- University of Limpopo, 2022 / The unique phytochemical composition of the medicinal plant cancer bush (Sutherlandia frutescens) have made its foliage to gain much attention in South Africa due to its health benefits. In situ harvesting of the plant parts of this important species serve as one potential strategy to avert its extinction through whole plant harvesting, a common practice by rural communities. However, such a strategy is limited by lack of information on the agronomic requirements of the plant species and its susceptibility to root-knot (Meloidogyne species) nematodes. The objectives of the study were four-fold, namely, to: (1) identify nodulation bacteria associated with wild S. frutescens using morphological and biochemical techniques, (2) assess the efficacy of the nodulation isolates from different centres of biodiversity of S. frutescens in Limpopo Province, South Africa (3) test the compatibility of cucurbitacin-containing phytonematicides on S. frutescens for managing population densities of Meloidogyne species and (4) determine the nutritional water productivity (NWP) of S. frutescens in association with water scarcity of the region where the plant species originated. In achieving Objective 1, nodules from S. frutescens roots were washed in distilled water and healthy, undamaged, firm and pink nodules were sterilised. Aseptic nodules from S. frutescens roots and commercial strains were transferred into a smasher biomerieux polythene bag containing 10 ml distilled water and crashed to produce a milky suspension the milky suspension was streaked on Yeast extract mannitol agar (YEMA). After gram reaction, colony characterisation includes the investigation of shape, colour, configuration, elevation and margin of bacterial colony as observed in colonies on nutrient agar plates of overnight grown microorganisms using a microscope. The medium for biochemical test was prepared, inoculated with 5 μl purified xxv bacterial cultures and incubated at 37°C for 48 h. Identification of the bacterial isolates was performed using VITEK 2 Systems (bioMérieux, Inc., North Carolina, USA). Using morphological and biochemical techniques, the bacterial species associated with roots of S. frutescens in the wild were assayed primarily those in the genera Raoutella ornithinolytica and Enterobacter cloacae species dissolvens. The VITEK 2 Systems confirmed the identification of the bacterial species from 80 to 96% of the samples. Three species were confirmed from another sampling area, Sphingomonas paucimobills, Raoutella ornithinolytica and Enterobacter cloacae species dissolvens from by 86 to 96% of the samples. In achieving Objective 2, the five treatments, namely, Bradyrhizobium spp. (Arachis) strain, Rhizobium leguminosarum strain, Tubatse strain, Sebayeng strain and untreated control, were laid-out in a randomised complete block design, with seven replications during the first season (Experiment 1) and with eight replications during the second season (Experiment 2). The seasonal interactions (Experiment 1 × Experiment 2) on plant and nutrient elements were not significant (P ≤ 0.05) and data for the two seasons were pooled (n = 75). Relative to untreated control, commercial (Bradyrhizobium and Rhizobium strain) and native strains (Tubatse and Sebayeng strain) significantly increased plant height by 31, 33, 44 and 40%, respectively, root length by 30, 41, 40 and 42%, respectively and dry shoot mass by 48,195 and 17%, respectively. Similarly, rhizobia strains significantly contributed to the increase in nitrogen assimilation by 7, 25 and 80%, respectively, protein synthesis by 13, 10, 24, 69%, respectively, and symbiotic efficiency by 31, 133, 292 and 82%, respectively. However, rhizobia inoculants had no significant effects on potassium and phosphorus in leaf tissues. In achieving Objective 3, in Mean Concentration Stimulation Point (MCSP) experiments, seven treatments, xxvi namely, 0, 2, 4, 8, 16, 32 and 64% for each phytonematicide, were arranged in a randomised complete block design (RCBD), with 8 replicates. In application interval experiments, treatments, based on “weeks-per-month-of-30 days” for M. javanica, which translated to 1, 2, 3 and 4 weeks, were arranged in a RCBD, with 10 replicates. Nemarioc-AL and Nemafric-BL phytonematicides had MCSP values of 3.43 and 4.03%, respectively, with the plant having high tolerance level to the products. The respective application interval of the two products for managing population densities of Meloidogyne species were 29 and 17 days. The dosage models for Nemarioc-AL and Nemafric-BL phytonematicides were 6.62 and 13.26%, respectively. In achieving Objective 5, the study used nine treatments designated as T1, T2, T3, T4, T5, T6, T7, T8 and T9, respectively, consisting of 1, 2, 3, 4, 5, 6, 7, 8 and 9 seedlings/hole of drip irrigation transplanted using a 3S planter under field conditions, arranged in randomised complete block design (RCBD) with 9 replications (n = 81) in two seasons. The NWP of total flavonoids, total tannin and total phenol exhibited positive quadratic relations in varied planting density suggesting that this cultural practices could be manipulated to improve NWP of cancer bush. In conclusion, the wild bacterial isolates, sampled from S. frutescens plant grown in the field, outperformed the commercial bacterial strains in enhancing the productivity of the test plants. The empirically established dosage model for Nemarioc-AL and Nemafric-BL phytonematicides could be used to control Meloidogyne species in cancer bush production. There is a need to further investigate the responses of the identified strains to the test phytonematicides. Findings of the study openend new frontiers in the development and commercialisation of the observed native bacterial strains for the cultivation of S. frutescens, which has excellent medicinal importance as a cure or management for cancer. / Agricultural Research Council-Universities Collaboration Centre, the National Research Foundation (NRF) and the Flemish Inter-University Council of Belgium

<p>This thesis is an introduction to virtual knots and the forbidden moves, and the closely related classes of welded and unwelded knots. Extensions of the Jones polynomial and the knot group to the various knot types are considered. We also examine the operation of connected sum for virtual and welded knots, and we review the proof that every virtual knot can be untied using the forbidden moves.</p> / Master of Science (MSc)

Field studies were conducted over two growing seasons to evaluate the effect of different levels of third instar European corn borer, Ostrinia nubilalis Hübner (Lepidoptera: Crambidae), on whole-plant dry matter in corn grown for silage. Mean (± SEM) whole-plant dry matter was significantly greater by 18.8% in uninfested control plants than in plants with an infestation level of 6 larvae/plant in 2004. Whole-plant dry matter in 2005 was significantly greater by 10.5% in control plants than in plants with an infestation level of 5 larvae/plant. Economic injury levels were calculated for each year using regression equations between whole-plant dry matter and European corn borer infestation level. Plant growth stage and infestation level had no effect on percent acid detergent fiber, neutral detergent fiber, and crude protein values for either year. Greenhouse studies were conducted to examine the relationship between aboveground herbivory by European corn borer and belowground herbivory by root knot nematode, Meloidogyne incognita Chitwood (Tylenchida: Heteroderidae), in corn. Two experiments were conducted to measure belowground herbivory by M. incognita in juvenile penetrations and eggs/root system. In the first experiment, the main effects interaction was not significant for either M. incognita juvenile penetrations or eggs/root system. Overall mean juvenile penetrations/root system across all three growth stages, at infestation levels of 1 and 3 larvae/plant were significantly less than in the non-infested control. In addition, overall mean eggs/root system at an infestation level of 3 larvae/plant were significantly less than in the control. In the second experiment, the main effects interaction was significant for both juvenile penetrations and eggs/root system. At the 8 and 10 leaf growth stages, juvenile penetrations/root system at infestation levels of 1 and 3 larvae/plant were significantly less than in the control. In addition, eggs/root system at an infestation level of 3 larvae/plant were significantly less than in the control, at all growth stages. In the reciprocal study, which examined the effect of different M. incognita inoculation levels on European corn borer stalk tunneling, no significant effect of inoculation level on European corn borer stalk tunneling was found. / Ph. D.

An investigation of the effect of Meloidogyne hapla, M. arenaria, M. arenaria thamesi, M. incognita acrita, and M. incognita on Ligustrum ovalifolium, L. japonicum, and Abelia floribunda was conducted. With the exception of M. hapla on L. ovalifolium and M. arenaria thamesi on A. floribunda, all 5 species of nematodes were pathogenic on the 3 host species. Striking differences in growth of the L. ovalifolium plants inoculated with the 4 root-knot species that caused significant reduction could easily be seen. Reduction in weight of the plants inoculated with the 4 root-knot species varied from 39.8% to 63.6% of the controls, and the reduction in total length of stems of these plants varied from 37.2% to 58.5% of the controls at the termination of the experiment. Reduction in weight of the L. japonicum plants inoculated with root-knot species varied from 29.2% to 51.7% of the controls. All plants inoculated with root-knot were significantly reduced in weight compared to controls. There were no visual differences in growth among the A. floribunda treatments; however, omitting the M. arenaria thamesi treatment which was not significantly different from control, the reduction in weight of the inoculated plants varied from 26.81 to 41.71 of the controls. / M.S.

This bachelor`s thesis present a study that is based on the castle garden at Tjolöholm Castle in Sweden. The focus is to examine which interesting changes and updates have been made. Many of them have happened in the last decade, others already happened during the time of the castle owners Blanche Dickson's lifetime. Her husband passed away prematurely and was basically not involved in the work of creating the garden. Mrs. Dickson, on the other hand, had the architect Lars Israel Wahlman to do it. He had been involved in the new construction of Tjolöholm's Castle and had thus gained the confidence to take on the castle garden. The planned knot garden at Tjolöholm was not laid out at the beginning of the 20th century because Blanche Dickson passed away very unexpectedly. The establishment of the knot garden therefore never happened then. Since Mrs. Dickson approved architect Wahlman's proposal with a knot garden, so she must have made sure that there was also one planned. But it didn't happen that way because of her passing. The management at Tjolöholm has been based on this knowledge and therefore it has been chosen to be construct. It turned out as Blanche Dickson wished and today it is part of the castle garden where it has now resulted in an interesting part of the well-visited and appreciated garden environment that is found at Tjolöholm Castle. Probably Mrs. Dickson would have preferred well-to-do and noble people who interested visitors to the knot garden. Today can you visit the castle garden. The study is carried out from physical existence with the guidance of Erwin Panofskys analysis method Ikonologi.

Title: Comparison of the physiological response rate of the organism using different one-rope ascent techniques Objectives: The aim of this study was to compare the rate of the physiological response of the organism using 3 different one-rope ascent techniques during constant speed. Methods: It was an empirically based study of experimental character (quasi-experiment). The measured research group (n = 12) consisted of the military students (21 ± 1.1 years; 183 ± 4.9 cm; 80.6 ± 7.8 kg) of full-time study at the Faculty of Physical Education and Sport of Charles University (VO FTVS UK). The physiological response rate was measured with the Cortex Metamax 3b and Polar sporttester during one-rope ascending techniques ("using Prusik knot" = P", "using jümar = B", "using Garda knot = G") at a constant speed of 3 m·min-1 for 7 minutes. The rating of the perceived exertion was also recorded on the Borg RPE scale. The data were comparatively analyzed in the SPSS statistic program, furthermore the analysis of variance (ANOVA) was also employed. Results: The study demonstrated statistical differences (p ≤ 0.05) between techniques: while B is the easiest, the greatest differences were observed between technique B, P and G. The G technigue appeared to be the most difficult. The average HR was: 162 ± 9 bpm...

We study two topics on surface diffeomorphisms, their mapping classes and dynamics. For the mapping classes of a punctured disc, we study the $\ZxZ$ subgroups of the fundamental groups of the corresponding mapping tori. An application is the proof of the fact that a satellite knot with braid pattern is prime. For the mapping classes of the disc minus a Cantor set, we study a special type of reducible mapping class. This has direct application on the embeddings of solenoids in $\mathbb{S}^3$. We also give some examples of other types of mapping classes of the disc minus a Cantor set. For the dynamics of surface diffeomorphisms, we prove three formulas for computing the topological pressure of a $C^1$-generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that there is no equilibrium states with positive measure theoretic entropy. In particular, for hyperbolic potentials, there are no equilibrium states. For $C^1$ generic conservative diffeomorphisms on compact surfaces with no dominated splitting and $\phi_m(x):=-\frac{1}{m}\log \Vert D_x f^m\Vert, m \in \mathbb{N}$, we show that there exist equilibrium states with zero entropy and there exists a transition point $t_0$ for the one parameter family $\lbrace t \phi_m\rbrace_{t\geq 0}$, such that there is no equilibrium states for $ t \in [0, t_0)$ and there is an equilibrium state for $t \in [t_0,+\infty)$.