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Water scarcity in the west has created a long history of conflict. When Utah was settled, laws were instituted (both officially and otherwise) that allowed water users to use streams and springs in efficient ways without causing harm to other users. The Provo River Decree is a physical example of local water law that has been in place for almost a hundred years. While many changes have arisen in its area of jurisdiction, it is still drawn upon to determine water rights. Ambiguity, rigidity, and overall changes to use patterns have limited the application of the decree to present situations. The current application of the Provo River Decree is therefore insufficient within the context of prior appropriation to deal with the fluid and changing nature of water use in the area. Additional research should be done to determine whether the system of prior appropriation in Utah is flexible enough to allow for changing use and human-controlled watercourses. This research should include an economic analysis on the impacts of free water right exchange on relative benefit of water rights as well as an analysis of the past and present impacts of external agencies on water use.

Determining the chromatic number of the partition graph P(33) poses a considerable challenge. We can bound it to 4 ≤ χ(P(33)) ≤ 6, with exhaustive search confirming χ(P(33)) = 6. A potential mathematical proof strategy for this equality involves identifying a Z2-invariant S4 with non-trivial homology in the box complex of the partition graph P(33), namely Bedge(︁P(33))︁, and applying the Borsuk-Ulam theorem to compute its Z2-index. This provides a robust topological lower bound for the chromatic number of P(33), termed the Lovász bound. We have verified the absence of such an S4 within certain sections of Bedge(︁P(33))︁. We also validated this approach through a case study on the Petersen graph. This thesis offers a thorough examination of various topological lower bounds for a graph’s chromatic number, complete with proofs and examples. We demonstrate instances where these lower bounds converge to a single value and others where they diverge significantly from a graph’s actual chromatic number. We also classify all vertex pairs, triples, and quadruples of P(33) into unique equivalence classes, facilitating the derivation of all maximal complete bipartite subgraphs. This classification informs the construction of all simplices of Bedge(︁P(33)). Following a detailed and technical exploration, we uncover both the maximal size of the pairwise intersections of its maximal simplices and their underlying structure. Our study proposes an algorithm for building the box complex of the partition graph P(33) using our method of identifying maximal complete bipartite subgraphs. This reduces time complexity to O(n3), marking a substantial enhancement over brute-force techniques. Lastly, we apply discrete Morse theory to construct a simplicial complex homotopy equivalent to the box complex of P(33), using two methods: elementary collapses and the determination of a discrete Morse function on the box complex. This process reduces the dimension of the box complex from 35 to 12, streamlining future calculations of the Z2-index and the Lovász bound.

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<p>This dissertation examined perturbation effects during complex tactile information transmission. The four experiments provide evidence regarding sensory and information processing demands in early stages of complex tactile learning.</p> <p>Experiment 1 established complex tactile learning behavioural performance. Vibrotactile stimuli representing Morse code letters were communicated to participants with or without induced perturbation to the finger of letter reception. Response performance was measured and augmented feedback was provided retroactively. Perturbation conditions lead to poor performance during tactile acquisition, but improved performance during application of knowledge.</p> <p>Experiment 2 determined if the experiment 1 results demonstrated masking or response competition paradigms. Target “masking” is the reduced ability to detect or interpret a stimuli pattern by presentation of other information (Craig, 1985; Verrillo, 1985). Response competition is the competition or distraction from target response generation by secondary stimuli (Craig, 2000; Bolanowski et al., 2000). Experiment 2 tested response competition by spatially separating the perturbation and tactile information delivery sites.</p> <p>Experiments 3 and 4 served to replicate behavioural acquisition data from experiments 1 and 2. They also extended the findings of the first two experiments by introducing neurophysiological measurement to reflect the changes associated with the two perturbation conditions. The study discerned whether the masking and response competition paradigms from experiments 1 and 2 were predominantly impacting the peripheral or central information processing.</p> <p>Results from the four studies collectively demonstrate that increased demands are placed on the sensory system during early stages of complex tactile learning when perturbation is spatially congruent with tactile information delivery. Experiments 1 and 2 revealed that attention does not supersede spatial location of perturbation, and perturbation location is paramount to yield sufficient interference to impede acquisition yet lead to enhanced knowledge retention and transfer. Experiments 3 and 4 determined that cortical information processing associated with complex tactile information acquisition are neurophysiologically differentiated when relative locations of meaningful and perturbation stimuli are congruent or spatially separated. The findings from this dissertation serve as an advancement of our understanding of masking and response competition phenomenon as they pertain to complex tactile learning.</p> / Doctor of Philosophy (PhD)

We study the nonlinear Schrödinger (NLS) equation on star graphs with the Neumann- Kirchhoff (NK) boundary conditions at the vertex. We analyze the stability of standing wave solutions of the NLS equation by using different techniques. We consider a half-soliton state of the NLS equation, and by using normal forms, we prove it is nonlinearly unstable due to small perturbations that grow slowly in time. Moreover, under certain constraints on parameters of the generalized NK conditions, we show the existence of a family of shifted states, which are parametrized by a translational parameter. We obtain the spectral stability/instability result for shifted states by using the Sturm theory for counting the Morse indices of the shifted states. For the spectrally stable shifted states, we show that the momentum of the NLS equation is not conserved which results in the irreversible drift of the family of shifted states towards the vertex of the star graph. As a result, the spectrally stable shifted states are nonlinearly unstable. We also study the NLS equation on star graphs with a delta-interaction at the vertex. The presence of the interaction modifies the NK boundary conditions by adding an extra parameter. Depending on the value of the parameter, the NLS equation admits symmetric and asymmetric standing waves with either monotonic or non-monotonic structure on each edge. By using the Sturm theory approach, we prove the orbital instability of the standing waves. / Thesis / Doctor of Philosophy (PhD)

No / Nonadiabatic Monte Carlo transition-state theory is used to explore competing C¿Cl and C¿Br bond fission processes in a simple model of 1[n,pi*(CO)] photoexcited bromoacetyl chloride. Morse potentials are used to represent bond stretching coordinates, and the positions and magnitudes of nonadiabatic coupling between excited state potentials are modeled using ab initio data. The main effect of nonadiabaticity is to favor C¿Cl fission over C¿Br, despite a larger barrier to C¿Cl dissociation. The absolute values of the rate constants are smaller than observed experimentally, but the calculated branching ratios are close to the experimental value. For C¿Cl fission, it is shown that the minimum energy crossing point is not sufficient to describe the rate constant, suggesting that care must be taken when using alternative models which make this assumption.

Titre de l'écran-titre (visionné le 11 janvier 2024) / Aujourd'hui, la cartographie des réseaux hydrographiques est un sujet important pour la gestion et l'aménagement de l'espace forestier, la prévention contre les risques d'inondation, etc. Les données sources pour cartographier les cours d'eau sont des nuages de points obtenus par des lidars aéroportés. Cependant, les méthodes d'extraction des réseaux usuelles nécessitent des opérations de découpage, de rééchantillonnage et d'assemblage des résultats pour produire un réseau complet, altérant la qualité des résultats et limitant l'automatisation des traitements. Afin de limiter ces opérations, une nouvelle approche d'extraction est considérée. Cette approche propose de construire un réseau de crêtes et de talwegs à partir des points lidar, puis transforme ce réseau en réseau hydrographique. Notre recherche consiste à concevoir une méthode d'extraction robuste du réseau adaptée aux données massives. Ainsi, nous proposons d'abord une approche de calcul du réseau adaptée aux surfaces triangulées garantissant la cohérence topologique du réseau. Nous proposons ensuite une architecture s'appuyant sur des conteneurs pour paralléliser les calculs et ainsi traiter des données massives. / Nowadays, the mapping of hydrographic networks is an important subject for forestry management and planning, flood risk prevention, and so on. The source data for mapping watercourses are point clouds obtained by airborne lidars. However, conventional network extraction methods require cutting, resampling, and assembling the results to produce a complete network, thereby altering the quality of the results, and limiting the automation of processing. In order avoid these processing steps, a new computational approach is considered. This approach involves building a network of ridges and talwegs from lidar points, and then transforming this network into a hydrographic network. Our research consists in designing a robust network extraction method adapted to massive data. First, we propose a network calculation approach adapted to triangulated surfaces, guaranteeing the network's topological consistency. We then propose a container-based architecture for parallelizing computations to handle big data processing.

Tableau d'honneur de la Faculté des études supérieures et postdoctorales, 2017-2018 / Dans ce mémoire, j’examine à travers les travaux du juriste et psychologue Stephen J. Morse la prétention selon laquelle les nouvelles connaissances issues des neurosciences sont appelées à transformer radicalement le droit criminel en fournissant des raisons d’abandonner la notion de responsabilité pénale. Le premier chapitre présente et critique l’idée que ces prétentions réformistes reposeraient sur des erreurs conceptuelles ou logiques. J’aborde aussi la thèse selon laquelle l’évaluation de la responsabilité criminelle repose sur des critères comportementaux insensibles aux données neuroscientifiques. Les chapitres suivants explorent deux manières par lesquelles les neurosciences transformeraient radicalement nos conceptions juridiques en mettant en doute la notion de responsabilité criminelle : par leur réfutation du libre arbitre et par leur conception de l’être humain comme un mécanisme biologique. Le deuxième chapitre s’interroge à savoir si le droit criminel présuppose le libre arbitre dans sa conception de la personne responsable. Je réponds négativement à cette question et argumente plutôt en faveur d’une conception de la responsabilité pénale fondée sur la possession de certaines capacités. Le troisième chapitre porte sur le rapport entre le droit et les explications mécanistes formulées en neurosciences. Certains craignent que si l’humain n’est qu’un mécanisme biologique, alors l’explication de l’action en termes d’états mentaux ne réfère à aucune réalité (éliminativisme par rapport aux états mentaux), ou du moins que les états mentaux ne figurent pas parmi les véritables causes de l’action (épiphénoménisme). Or, la réalité des états mentaux et leur efficacité causale sont des présupposés essentiels du droit criminel. Je soutiens que la solution de Morse, ancrée dans une théorie non réductionniste de l’esprit, repose sur une confusion et ne permet pas de répondre à ces défis. Le droit criminel devrait plutôt miser sur une approche réductionniste, non éliminative, s’il entend entretenir une relation harmonieuse avec les neurosciences. / Some argue that neuroscience will have radical implications for the law. For instance, by identifying the brain-based causes of behaviour, neuroscience would rule out free will and consequently, make moral and criminal responsibility concepts and practices obsolete. In this MA thesis, I tackle this issue through the work of legal scholar and psychologist Stephen J. Morse. Chapter 1 critically assesses the “hard conservative” theses that reformist assumptions rely on conceptual and logical mistakes such as the naturalistic fallacy, the mereological fallacy or category errors, and that behavioral evidence always prevails over neuroscientific evidence. Subsequent chapters explore two ways neuroscience is taken to imply radical modifications to our legal responsibility concepts and practices: through its denial of free will and through its depiction of human beings as natural, biological mechanisms. Chapter 2 addresses the question whether the legal conception of a responsible person presupposes free will. I answer this question negatively and further argue that responsibility tracks mental capacity, not free will. Chapter 3 focuses on the mechanistic explanations in neuroscience and their implications for the law. The challenge is that, allegedly, if we humans only are biological mechanisms, then either mental states and agency more generally are not real (eliminativism) or they are real but have no causal power (epiphenomenalism). In both case, the legal conception of the responsible person is thoroughly problematic since it presupposes that persons really have intentions, desires, beliefs, and the like, and that these mental states can cause actions. I argue that Morse is wrong in relying on a non-reductionist theory of mind in his answer to this challenge since it rests on a confusion concerning reductivism. Thus, criminal law’s conception of a responsible person would be better defended through a reductionist, non-eliminative approach.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.