Diagnosis of the nutrient compositional space of fruit crops

Tissue analysis is a useful tool for the nutrient management of fruit orchards. The mineral composition of diagnostic tissues expressed as nutrient concentration on a dry weight basis has long been used to assess the status of 'pure' nutrients. When nutrients are mixed and interact in plant tissues, their proportions or concentrations change relatively to each other as a result of synergism, antagonism, or neutrality, hence producing resonance within the closed space of tissue composition. Ternary diagrams and nutrient ratios are early representations of interacting nutrients in the compositional space. Dual and multiple interactions were integrated by the Diagnosis and Recommendation Integrated System (DRIS) into nutrient indexes and by Compositional Nutrient Diagnosis into centered log ratios (CND-clr). DRIS has some computational flaws such as using a dry matter index that is not a part as well as nutrient products (e.g. NxCa) instead of ratios. DRIS and CND-clr integrate all possible nutrient interactions without defining an ad hoc interactive model. They diagnose D components while D-1 could be diagnosed in the D-compositional Hilbert space. The isometric log ratio (ilr) coordinates overcome these problems using orthonormal binary nutrient partitions instead of dual ratios. In this study, it is presented a nutrient interactive model as well as computation methods for DRIS and CND-clr and CND-ilr coordinates (CND-ilr) using leaf analytical data from an experimental apple orchard in Southwestern Quebec, Canada. It was computed the Aitchison and Mahalanobis distances across ilr coordinates as measures of nutrient imbalance. The effect of changing nutrient concentrations on ilr coordinates are simulated to identify the ones contributing the most to nutrient imbalance.

Representations of swinging London in 1960s British cinema : Blowup (1966), Smashing Time (1967), and Performance (1970)

This thesis explores the representation of Swinging London in three examples of 1960s British cinema: Blowup (Michelangelo Antonioni, 1966), Smashing Time (Desmond Davis, 1967) and Performance (Donald Cammell and Nicolas Roeg, 1970). It suggests that the films chronologically signify the evolution, commodification and dissolution of the Swinging London era. The thesis explores how the concept of Swinging London is both critiqued and perpetuated in each film through the use of visual tropes: the reconstruction of London as a cinematic space; the Pop photographer; the dolly; representations of music performance and fashion; the appropriation of signs and symbols associated with the visual culture of Swinging London. Using fashion, music performance, consumerism and cultural symbolism as visual narratives, each film also explores the construction of youth identity through the representation of manufactured and mediated images. Ultimately, these films reinforce Swinging London as a visual economy that circulates media images as commodities within a system of exchange. With this in view, the signs and symbols that comprise the visual culture of Swinging London are as central and significant to the cultural era as their material reality. While they attempt to destabilize prevailing representations of the era through the reproduction and exchange of such symbols, Blowup, Smashing Time, and Performance nevertheless contribute to the nostalgia for Swinging London in larger cultural memory.

The Gandarela Mountain Range and the “resistance space” against iron ore mining threat: a focus on the contrapositions

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Telefantasy tower blocks: space, place and social realism shake-ups in Misfits

This article considers the ways in which British youth telefantasy Misfits (E4, 2009–13) takes up and makes strange urban spaces familiar from social-realist narratives. Filmed on the sprawling East London estate, Thamesmead, the programme chronicles a group of young offenders who are given powers by a freak storm, turning them into ‘ASBO superheroes’. Misfits depends on its British urban landscapes for the assertion of its ‘authenticity’ within British youth television, using spaces and landscapes familiar from urban youth exploitation cinema and television's narratives of the underclass. After situating the series within existing cultural discourses and recent developments in social-realist representations, the article explores how Misfits disrupts what have become signifiers for the ‘real’ – the brutalism of housing estates, the grey of the concrete and sky – by making them strange, turning them into telefantasy. The series presents the estate as an uncanny place: the domestic, social-realist world shifted into a fantastical space by the storm. Through close analysis, this article explores how the familiar spaces become skewed and unsettling to match our protagonists' isolation, shifting bodies and scrambled sense of self.

Space, authenticity and utopia in the hip-hop teen dance film

The dance film flourished in the 2000s in the form of the hip-hop teen dance film. Such films as Save the Last Dance (Thomas Carter, 2001), Honey (Billy Woodruff, 2002) and Step Up (Anne Fletcher, 2006) drew on hip-hop’s dominance of the mainstream music industry and combined the teen film’s pre-existing social problem and musical narratives. Yet various tension were created by their interweaving of representations of post-industrial city youth with the utopian sensibilities of the classical Hollywood musical. Their narratives celebrated hip-hop performance, and depicted dance’s ability to bridge cultural boundaries and bring together couples and communities. These films used hip-hop to define space and identity yet often constructed divisions within their soundscapes, limiting hip-hop’s expressive potential. This article explores the cycle’s celebration of, yet struggle with, hip-hop through examining select films’ interactions between soundscape, narrative and form. It will engage with these films’ attempts to marry the representational, narrative and aesthetic meanings of hip-hop culture with the form and ideologies of the musical genre, particularly the tensions and continuities that arise from their engagement with the genre’s utopian qualities identified by Richard Dyer (1985). Yet whilst these films illustrate the tensions and challenges of combining hip-hop culture and the musical genre, they also demonstrate an effective integration of hip-hop soundscape and the dancing body in their depiction of dance, highlighting both form’s aesthetics of layering, rupture and flow (Rose, 1994: 22).

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Pion: space-like structure

The scalar form factor describes modifications induced by the pion over the quark condensate. Assuming that representations produced by chiral perturbation theory can be pushed to high values of negative-t, a region in configuration space is reached (r < R similar to 0.5 fm) where the form factor changes sign, indicating that the condensate has turned into empty space. A simple model for the pion incorporates this feature into density functions. When supplemented by scalar-meson excitations, it yields predictions close to empirical values for the mean square radius (< r(2)>(pi)(S) = 0.59 fm(2)) and for one of the low energy constants ((l) over bar (4) = 4.3), with no adjusted parameters.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Localizability in de Sitter space

An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of the de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. Representations in both the principal and the complementary series are considered. A simple expression for the time evolution of the Newton-Wigner operator is presented.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.