Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

Canopy processes, fluxes and microclimate in a pine forest

Interaction between forests and the atmosphere occurs by radiative and turbulent transport. The fluxes of energy and mass between surface and the atmosphere directly influence the properties of the lower atmosphere and in longer time scales the global climate. Boreal forest ecosystems are central in the global climate system, and its responses to human activities, because they are significant sources and sinks of greenhouse gases and of aerosol particles. The aim of the present work was to improve our understanding on the existing interplay between biologically active canopy, microenvironment and turbulent flow and quantify. In specific, the aim was to quantify the contribution of different canopy layers to whole forest fluxes. For this purpose, long-term micrometeorological and ecological measurements made in a Scots pine (Pinus sylvestris) forest at SMEAR II research station in Southern Finland were used. The properties of turbulent flow are strongly modified by the interaction between the canopy elements: momentum is efficiently absorbed in the upper layers of the canopy, mean wind speed and turbulence intensities decrease rapidly towards the forest floor and power spectra is modulated by spectral short-cut . In the relative open forest, diabatic stability above the canopy explained much of the changes in velocity statistics within the canopy except in strongly stable stratification. Large eddies, ranging from tens to hundred meters in size, were responsible for the major fraction of turbulent transport between a forest and the atmosphere. Because of this, the eddy-covariance (EC) method proved to be successful for measuring energy and mass exchange inside a forest canopy with exception of strongly stable conditions. Vertical variations of within canopy microclimate, light attenuation in particular, affect strongly the assimilation and transpiration rates. According to model simulations, assimilation rate decreases with height more rapidly than stomatal conductance (gs) and transpiration and, consequently, the vertical source-sink distributions for carbon dioxide (CO2) and water vapor (H2O) diverge. Upscaling from a shoot scale to canopy scale was found to be sensitive to chosen stomatal control description. The upscaled canopy level CO2 fluxes can vary as much as 15 % and H2O fluxes 30 % even if the gs models are calibrated against same leaf-level dataset. A pine forest has distinct overstory and understory layers, which both contribute significantly to canopy scale fluxes. The forest floor vegetation and soil accounted between 18 and 25 % of evapotranspiration and between 10 and 20 % of sensible heat exchange. Forest floor was also an important deposition surface for aerosol particles; between 10 and 35 % of dry deposition of particles within size range 10 30 nm occurred there. Because of the northern latitudes, seasonal cycle of climatic factors strongly influence the surface fluxes. Besides the seasonal constraints, partitioning of available energy to sensible and latent heat depends, through stomatal control, on the physiological state of the vegetation. In spring, available energy is consumed mainly as sensible heat and latent heat flux peaked about two months later, in July August. On the other hand, annual evapotranspiration remains rather stable over range of environmental conditions and thus any increase of accumulated radiation affects primarily the sensible heat exchange. Finally, autumn temperature had strong effect on ecosystem respiration but its influence on photosynthetic CO2 uptake was restricted by low radiation levels. Therefore, the projected autumn warming in the coming decades will presumably reduce the positive effects of earlier spring recovery in terms of carbon uptake potential of boreal forests.

Atmospheric factors governing banded orographic convection

Atmospheric factors Governing Banded Orographic Convection The three-dimensional structure of shallow orographic convection is investigated through simulations performed with a cloud-resolving numerical model. In moist flows that overcome a given topographic barrier to form statically unstable cap clouds, the organization of the convection depends on both the atmospheric structure and the mechanism by which the convection is initiated. Convection initiated by background thermal fluctuations embedded in the flow over a smooth mountain (without any small-scale topographic features) tends to be cellular and disorganized except that shear-parallel bands may form in flows with strong unidirectional vertical shear. The development of well-organized bands is favored when there is weak static instability inside the cloud and when the dry air surrounding the cloud is strongly stable. These bands move with the flow and distribute their cumulative precipitation evenly over the mountain upslope. Similar shear-parallel bands also develop in flows where convection is initiated by small-scale topographic noise superimposed onto the main mountain profile, but in this case stronger circulations are also triggered that create stationary rainbands parallel to the low-level flow. This second dominant mode, which is less sensitive to the atmospheric structure and the strength of forcing, is triggered by lee waves that form over small-scale topographic bumps near the upstream edge of the main orographic cloud. Due to their stationarity, these flow-parallel bands can produce locally heavy precipitation amounts.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

Strong primeness in fuzzy environment

The main aim of this investigation is to propose the notion of uniform and strong primeness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primeness in fuzzy. Second, a fuzzy version of correspondence theorem and the radical of a fuzzy ideal are proposed. Finally, it is proposed a new concept of prime ideal for Quantales which enable us to deal with primeness in a noncommutative setting.

Strong primeness in fuzzy environment

The main aim of this investigation is to propose the notion of uniform and strong primeness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primeness in fuzzy. Second, a fuzzy version of correspondence theorem and the radical of a fuzzy ideal are proposed. Finally, it is proposed a new concept of prime ideal for Quantales which enable us to deal with primeness in a noncommutative setting.

Crosstalk between developmental and tumour-specific signalling pathways : kallikrein-related serine peptidases and nodal in prostrate cancer

Prostate cancer is an important male health issue. The strategies used to diagnose and treat prostate cancer underscore the cell and molecular interactions that promote disease progression. Prostate cancer is histologically defined by increasingly undifferentiated tumour cells and therapeutically targeted by androgen ablation. Even as the normal glandular architecture of the adult prostate is lost, prostate cancer cells remain dependent on the androgen receptor (AR) for growth and survival. This project focused on androgen-regulated gene expression, altered cellular differentiation, and the nexus between these two concepts. The AR controls prostate development, homeostasis and cancer progression by regulating the expression of downstream genes. Kallikrein-related serine peptidases are prominent transcriptional targets of AR in the adult prostate. Kallikrein 3 (KLK3), which is commonly referred to as prostate-specific antigen, is the current serum biomarker for prostate cancer. Other kallikreins are potential adjunct biomarkers. As secreted proteases, kallikreins act through enzyme cascades that may modulate the prostate cancer microenvironment. Both as a panel of biomarkers and cascade of proteases, the roles of kallikreins are interconnected. Yet the expression and regulation of different kallikreins in prostate cancer has not been compared. In this study, a spectrum of prostate cell lines was used to evaluate the expression profile of all 15 members of the kallikrein family. A cluster of genes was co-ordinately expressed in androgenresponsive cell lines. This group of kallikreins included KLK2, 3, 4 and 15, which are located adjacent to one another at the centromeric end of the kallikrein locus. KLK14 was also of interest, because it was ubiquitously expressed among the prostate cell lines. Immunohistochemistry showed that these 5 kallikreins are co-expressed in benign and malignant prostate tissue. The androgen-regulated expression of KLK2 and KLK3 is well-characterised, but has not been compared with other kallikreins. Therefore, KLK2, 3, 4, 14 and 15 expression were all measured in time course and dose response experiments with androgens, AR-antagonist treatments, hormone deprivation experiments and cells transfected with AR siRNA. Collectively, these experiments demonstrated that prostatic kallikreins are specifically and directly regulated by the AR. The data also revealed that kallikrein genes are differentially regulated by androgens; KLK2 and KLK3 were strongly up-regulated, KLK4 and KLK15 were modestly up-regulated, and KLK14 was repressed. Notably, KLK14 is located at the telomeric end of the kallikrein locus, far away from the centromeric cluster of kallikreins that are stimulated by androgens. These results show that the expression of KLK2, 3, 4, 14 and 15 is maintained in prostate cancer, but that these genes exhibit different responses to androgens. This makes the kallikrein locus an ideal model to investigate AR signalling. The increasingly dedifferentiated phenotype of aggressive prostate cancer cells is accompanied by the re-expression of signalling molecules that are usually expressed during embryogenesis and foetal tissue development. The Wnt pathway is one developmental cascade that is reactivated in prostate cancer. The canonical Wnt cascade regulates the intracellular levels of β-catenin, a potent transcriptional co-activator of T-cell factor (TCF) transcription factors. Notably, β-catenin can also bind to the AR and synergistically stimulate androgen-mediated gene expression. This is at the expense of typical Wnt/TCF target genes, because the AR:β-catenin and TCF:β-catenin interactions are mutually exclusive. The effect of β-catenin on kallikrein expression was examined to further investigate the role of β-catenin in prostate cancer. Stable knockdown of β-catenin in LNCaP prostate cancer cells attenuated the androgen-regulated expression of KLK2, 3, 4 and 15, but not KLK14. To test whether KLK14 is instead a TCF:β-catenin target gene, the endogenous levels of β-catenin were increased by inhibiting its degradation. Although KLK14 expression was up-regulated by these treatments, siRNA knockdown of β-catenin demonstrated that this effect was independent of β-catenin. These results show that β-catenin is required for maximal expression of KLK2, 3, 4 and 15, but not KLK14. Developmental cells and tumour cells express a similar repertoire of signalling molecules, which means that these different cell types are responsive to one another. Previous reports have shown that stem cells and foetal tissues can reprogram aggressive cancer cells to less aggressive phenotypes by restoring the balance to developmental signalling pathways that are highly dysregulated in cancer. To investigate this phenomenon in prostate cancer, DU145 and PC-3 prostate cancer cells were cultured on matrices pre-conditioned with human embryonic stem cells (hESCs). Soft agar assays showed that prostate cancer cells exposed to hESC conditioned matrices had reduced clonogenicity compared with cells harvested from control matrices. A recent study demonstrated that this effect was partially due to hESC-derived Lefty, an antagonist of Nodal. A member of the transforming growth factor β (TGFβ) superfamily, Nodal regulates embryogenesis and is re-expressed in cancer. The role of Nodal in prostate cancer has not previously been reported. Therefore, the expression and function of the Nodal signalling pathway in prostate cancer was investigated. Western blots confirmed that Nodal is expressed in DU145 and PC-3 cells. Immunohistochemistry revealed greater expression of Nodal in malignant versus benign glands. Notably, the Nodal inhibitor, Lefty, was not expressed at the mRNA level in any prostate cell lines tested. The Nodal signalling pathway is functionally active in prostate cancer cells. Recombinant Nodal treatments triggered downstream phosphorylation of Smad2 in DU145 and LNCaP cells, and stably-transfected Nodal increased the clonogencity of LNCaP cells. Nodal was also found to modulate AR signalling. Nodal reduced the activity of an androgen-regulated KLK3 promoter construct in luciferase assays and attenuated the endogenous expression of AR target genes including prostatic kallikreins. These results demonstrate that Nodal is a novel example of a developmental signalling molecule that is reexpressed in prostate cancer and may have a functional role in prostate cancer progression. In summary, this project clarifies the role of androgens and changing cellular differentiation in prostate cancer by characterising the expression and function of the downstream genes encoding kallikrein-related serine proteases and Nodal. Furthermore, this study emphasises the similarities between prostate cancer and early development, and the crosstalk between developmental signalling pathways and the AR axis. The outcomes of this project also affirm the utility of the kallikrein locus as a model system to monitor tumour progression and the phenotype of prostate cancer cells.

Self-assembled hyperbranched polymer - gold nanoparticle hybrids : understanding the effect of polymer coverage on assembly size and SERS performance

In the past few years, remarkable progress has been made in unveiling novel and unique optical properties of strongly coupled plasmonic nanostructures. However, application of such plasmonic nanostructures in biomedicine remains challenging due to the lack of facile and robust assembly methods for producing stable nanostructures. Previous attempts to achieve plasmonic nano-assemblies using molecular ligands were limited due to the lack of flexibility that could be exercised in forming them. Here, we report the utilization of tailor-made hyperbranched polymers (HBP) as linkers to assemble gold nanoparticles (NPs) into nano-assemblies. The ease and flexibility in tuning the particle size and number of branch ends of a HBP makes it an ideal candidate as a linker, as opposed to DNA, small organic molecules and linear or dendrimeric polymers. We report a strong correlation of polymer (HBP) concentration with the size of the hybrid nano-assemblies and “hot-spot” density. We have shown that such solutions of stable HBP-gold nano-assemblies can be barcoded with various Raman tags to provide improved surface-enhanced Raman scattering (SERS) compared with non-aggregated NP systems. These Raman barcoded hybrid nano-assemblies, with further optimization of NP shape, size and “hot-spot” density, may find application as diagnostic tools in nanomedicine.

Environmental and climatic dependences of stable isotope ratios in tree rings on different temporal scales

This work examines stable isotope ratios of carbon, oxygen and hydrogen in annual growth rings of trees. Isotopic composition in wood cellulose is used as a tool to study past climate. The method benefits from the accurate and precise dating provided by dendrochronology. In this study the origin, nature and the strength of climatic correlations are studied on different temporal scales and at different sites in Finland. The origin of carbon isotopic signal is in photosynthetic fractionation. The basic physical and chemical fractionations involved are reasonably well understood. This was confirmed by measuring instantaneous photosynthetic discrimination on Scots pine (Pinus sylvestris L.). The internal conductance of CO2 was recognized to have a significant impact on the observed fractionation, and further investigations are suggested to quantify its role in controlling the isotopic signal of photosynthates. Isotopic composition of the produced biomass can potentially be affected by variety of external factors that induce physiological changes in trees. Response of carbon isotopic signal in tree ring cellulose to changes in resource availability was assessed in a manipulation experiment. It showed that the signal was relatively stable despite of changes in water and nitrogen availability to the tree. Palaeoclimatic reconstructions are typically based on functions describing empirical relationship between isotopic and climatic parameters. These empirical relationships may change depending on the site conditions, species and timeframe studied. Annual variation in Scots pine tree ring carbon and oxygen isotopic composition was studied in northern and in central eastern Finland and annual variation in tree ring latewood carbon, oxygen and hydrogen isotopic ratio in Oak (Quercus robur L.) was studied in southern Finland. In all of the studied sites at least one of the studied isotope ratios was shown to record climate strongly enough to be used in climatic reconstructions. Using the observed relationships, four-century-long climate reconstructions from living Scots pine were created for northern and central eastern Finland. Also temporal stability of the relationships between three proxy indicators, tree ring growth and carbon and oxygen isotopic composition was studied during the four-hundred-year period. Isotope ratios measured from tree rings in Finland were shown to be sensitive indicators of climate. Increasing understanding of environmental controls and physiological mechanisms affecting tree ring isotopic composition will make possible more accurate interpretation of isotope data. This study also demonstrated that by measuring multiple isotopes and physical proxies from the same tree rings, additional information on tree physiology can be obtained. Thus isotopic ratios measured from tree ring cellulose provide means to improve the reliability of climate reconstructions.

Highly luminescent and thermally stable lanthanide coordination polymers designed from 4-(dipyridin-2-yl)aminobenzoate: efficient energy transfer from Tb3+ to Eu3+ in a mixed lanthanide coordination compound

Herein, a new aromatic carboxylate ligand, namely, 4-(dipyridin-2-yl)aminobenzoic acid (HL), has been designed and employed for the construction of a series of lanthanide complexes (Eu3+ = 1, Tb3+ = 2, and Gd3+ = 3). Complexes of 1 and 2 were structurally authenticated by single-crystal X-ray diffraction and were found to exist as infinite 1D coordination polymers with the general formulas {Eu(L)(3)(H2O)(2)]}(n) (1) and {Tb(L)(3)(H2O)]center dot(H2O)}(n) (2). Both compounds crystallize in monoclinic space group C2/c. The photophysical properties demonstrated that the developed 4-(dipyridin-2-yl)aminobenzoate ligand is well suited for the sensitization of Tb3+ emission (Phi(overall) = 64%) thanks to the favorable position of the triplet state ((3)pi pi*) of the ligand the energy difference between the triplet state of the ligand and the excited state of Tb3+ (Delta E) = (3)pi pi* - D-5(4) = 3197 cm(-1)], as investigated in the Gd3+ complex. On the other hand, the corresponding Eu3+ complex shows weak luminescence efficiency (Phi(overall) = 7%) due to poor matching of the triplet state of the ligand with that of the emissive excited states of the metal ion (Delta E = (3)pi pi* - D-5(0) = 6447 cm(-1)). Furthermore, in the present work, a mixed lanthanide system featuring Eu3+ and Tb3+ ions with the general formula {Eu0.5Tb0.5(L)(3)(H2O)(2)]}(n) (4) was also synthesized, and the luminescent properties were evaluated and compared with those of the analogous single-lanthanide-ion systems (1 and 2). The lifetime measurements for 4 strongly support the premise that efficient energy transfer occurs between Tb3+ and Eu3+ in a mixed lanthanide system (eta = 86%).

Stable and Potent Analogues Derived from the Modification of the Dicarbonyl Moiety of Curcumin

Curcumin has shown promising therapeutic utilities for many diseases, including cancer; however, its clinical application is severely limited because of its poor stability under physiological conditions. Here we find that curcumin also loses its activity instantaneously in a reducing environment. Curcumin can exist in solution as a tautomeric mixture of keto and enol forms, and the enol form was found to be responsible for the rapid degradation of the compound. To increase the stability of curcumin, several analogues were synthesized in which the diketone moiety of curcumin was replaced by isoxazole (compound 2) and pyrazole (compound 3) groups. Isoxazole and pyrazole curcumins were found to be extremely stable at physiological pH, in addition to reducing atmosphere, and they can kill cancer cells under serum-depleted condition. Using molecular modeling, we found that both compounds 2 and 3 could dock to the same site of tubulin as the parent molecule, curcumin. Interestingly, compounds 2 and 3 also show better free radical scavenging activity than curcumin. Altogether, these results strongly suggest that compounds 2 and 3 could be good replacements for curcumin in future drug development.

Microwave spectroscopic and theoretical investigations of the strongly hydrogen bonded hexafluoroisopropanol...water complex

This paper reports microwave spectroscopic and theoretical investigations on the interaction of water with hexafluoroisopropanol (HFIP). The HFIP monomer can exist in two conformations, antiperiplanar (AP) and synclinical (SC). The former is about 5 kJ mol(-1) more stable than the latter. Theoretical calculations predicted three potential minima for the complex, two having AP and one having SC conformations. Though, the binding energy for the HFIP(SC)...H2O turned out to be larger than that for the other two conformers having HFIP in the AP form, the global minimum for the complex in the potential energy hypersurface had HFIP in the AP form. Experimental rotational constants for four isotopologues measured using a pulsed nozzle Fourier transform microwave spectrometer, correspond to the global minimum in the potential energy hypersurface. The structural parameters and the internal dynamics of the complex could be determined from the rotational spectra of the four isotopologues. The global minimum has the HFIP(AP) as a hydrogen bond donor forming a strong hydrogen bond with H2O. To characterize the strength of the bonding and to probe the other interactions within the complex, atoms in molecules, non-covalent interaction index and natural bond orbital theoretical analyses have been performed.

GRMHD formulation of highly super-Chandrasekhar rotating magnetized white dwarfs: stable configurations of non-spherical white dwarfs

Here we extend the exploration of significantly super-Chandrasekhar magnetized white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetized polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetized axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2-3 solar mass, with central (deep interior) magnetic fields of the order of 10(14) G and differential rotation with surface time periods of about 1-10 s. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous Type Ia supernovae, to which observational evidence ascribes mass in the range 2.1-2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.