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    (1 + ε) moments suffice to characterise the GFF
    (Electronic Journal of Probability, 2021) Berestycki, Nathanaël; Powell, Ellen; Ray, Gourab
    We show that there is “no stable free field of index α∈ (1,2)”, in the following sense. It was proved in [4] that subject to a fourth moment assumption, any random generalised function on a domain D of the plane, satisfying conformal invariance and a natural domain Markov property, must be a constant multiple of the Gaussian free field. In this article we show that the existence of (1+𝜀) moments is sufficient for the same conclusion. A key idea is a new way of exploring the field, where (instead of looking at the more standard circle averages) we start from the boundary and discover averages of the field with respect to a certain “hitting density” of Itô excursions.
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    1-D and 2-D digital filters design using model reduction and optimization methods for broadband beamforming and interference rejection
    (2025) Omar, Abdussalam; Agathoklis, Panajotis; Shpak, Dale John
    This thesis presents several design algorithms for nearly linear-phase one-dimensional (1-D) and two-dimensional (2-D) infinite impulse response (IIR) digital filters. Optimization techniques as well as model order reduction (MOR) filter design methods are considered in this study. For 1-D, finite impulse response (FIR) filters can achieve perfectly linear phase which makes them important in applications such as the field of audio signal processing where a flat delay characteristic may be desired. However, in most applications a perfectly linear phase response is not required and filters that have nearly linear phase response are quite acceptable. In such cases, IIR filters are more attractive than FIR filters. The design of IIR filters is more challenging than that of FIR filters because it results in a highly nonlinear objective function that requires sophisticated optimization methods. The 1-D optimization method proposed here solves the problem of approximating specified magnitude and linear-phase responses simultaneously. Since IIR filters can be designed to have nearly linear phase response in the passband, their passband group delay is usually considerably smaller than the delay of linear-phase FIR filters with equivalent magnitude responses. Meeting a required minimum stopband attenuation or a minimum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by the proposed optimization method for 1-D IIR filter. Also, an important constraint in the design of IIR filters is the prescription of a maximum pole radius, which allows to guarantee the stability margin and low coefficient selectivity for the obtained filter for finite-precision implementations. These design specifications are consistent with the constraints which often arise in practical filter design problems. In this research work, an optimization method for solving this constrained 1-D IIR design problem is presented. The above optimization method used for designing 1-D IIR filters is extended to 2-D separable-denominator IIR digital filters with nearly linear phase in the passband. During the development of the proposed design techniques for 2-D digital filters, a special emphasis has been placed on their computational efficiency and a method for the design of 2-D IIR digital filters based on a balanced realization (BR) model order reduction technique is proposed. In this method, the initial design is a linear phase 2-D FIR filter realized in a 2-D state space model, which leads to a stable 2-D separable-denominator IIR filter with nearly linear phase in the passband. The model reduction method is based on structured controllability Ps and structured observability Qs gramians. These gramians are block-diagonal positive-definite matrices satisfying 2-D Lyapunov inequalities. An efficient general algorithm is developed to compute these matrices by minimizing the trace of Ps and the trace of Qs under Linear Matrix Inequalities (LMI) constraints. The use of these gramians ensures that the resulting 2-D IIR filter is a 2-D stable filter. Furthermore, the obtained nearly linear-phase 2-D IIR filter is more economical and computationally more efficient than the original 2-D FIR filter. Numerical examples using MATLAB show that the proposed method provides a good compromise between the filter selectivity and computational complexity when compared to existing techniques, making the results of this dissertation directly applicable to many practical applications. For example, in the field of array signal processing, 2-D digital filters having a fan-shaped filter in the passband emerge as powerful tools, particularly when employed as beamformers in scenarios where the Direction of Arrivals (DOAs) of the desired broadband Plane Waves (PWs) are known. In such cases, the designed 2-D FIR and IIR filters having a fan-shaped filter passband in the 2-D frequency domains are used as beamformers. Benefiting from the knowledge of DOAs of the desired broadband PWs, these filters are used to extract the signal of interest (SOI), suppress the interference, and reduce the noise corrupting the SOI. The successful implementation of 2-D FIR and IIR fan filters as beamformers not only enhances the rejection of the interference but also demonstrates its capability to reduce the effect of AWGN. This dual functionality holds significant implications for practical applications in digital signal processing, in which robustness against interference and noise is important. Simulation results demonstrate a good performance of the proposed beamformers and confirmed that the filters obtained using the proposed methods are capable of extracting and enhancing the desired 2-D broadband signals according to their directions of arrival under severe interference and noise.
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    A 10 kW ZVS Integrated Boost Dual Three-Phase Bridge DC–DC Resonant Converter for a Linear Generator-Based Wave-Energy System: Design and Simulation
    (Electronics, 2019) Harischandrappa, Nagendrappa; Bhat, Ashoka K. S.
    The design and performance analysis of a 10 kW three-phase DC–DC LCL-type resonant converter having a built-in boost function were carried out. This high-power converter is proposed for its application in grid-interfacing a linear generator (LG)-based wave-energy system. Fixed-frequency control is used, and the converter was designed to operate with a lagging power factor. It is shown that all switches turn on with zero-voltage switching (ZVS) for wide input voltage and load variations. This results in reduced switching losses and stresses, which is very important in large-power applications. The performance of the converter was studied through PSIM simulation software. Theoretical and simulation results are presented for comparison. Power-loss break-down analysis of the designed converter was carried out and the summary of results is presented.
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    10,000 Steps a Day to Decrease Chronic Disease Risk Factors and Increase Aerobic Physical Activity Levels Among Capital Regional District Office Workers in Victoria, BC.
    (2013-04-30) Delaney, Kara; Stuart-Hill, Lynneth A.
    The mixed method design examined the impact of a 6-week pedometer based 10,000 moderate-vigorous steps a day employee workplace wellness challenge on aerobic fitness, chronic disease markers, and self-reported physical activity. The study used prompts to both educate and facilitate the intervention. Pre and post-test data analyzed self-report physical activity and sedentary time, sub max aerobic walking levels, and anthropometric measures. Participants logged their step count across the intervention and were challenged to increase their steps throughout. Participants were on average unable to achieve the goal step count and thus no statistically significance was found between pre-post tests. Qualitatively, three themes emerged from discussions with participants about their experiences: awareness of physical activity (PA) levels, demands of both work and family, and the frequency and content of the information given as prompts. The combination of prompts and the pedometer created an awareness of PA levels among participants but failed to fully motivate them to hit their target step count.
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    10,000 years later: body shape and evolution in threespine stickleback
    (2009-12-08T23:14:28Z) Spoljaric, Mark A.; Reimchen, T. E.
    Descent with modification (Darwin, 1859) overwhelmingly occurs through the process of natural selection on genetically variable traits. Following deglaciation in the Pleistocene, morphologically conservative marine stickleback (Gasterosteus aculeatus) from two distinct mitochondrial DNA lineages colonized freshwater habitats on the Haida Gwaii archipelago. These freshwater populations have radiated in response to a diverse selective landscape on the archipelago and exhibit morphological diversity that equals or exceeds the known range for the species in the circumboreal distribution. I investigated the body shape of 3808 stickleback from 125 isolated populations from Haida Gwaii using geometric morphometrics. Relative warp and discriminant function analysis were used to quantify lateral shape differences based on partial warp scores. which were generated from twelve homologous landmarks digitally placed on each specimen's image. The possibility of ontogenetic shifts and sexual dimorphism of body shape were examined for each population on the archipelago. Stickleback body-shape changes during ontogeny were highly variable, and cannot be predicted by the volume and water clarity of the habitat. I found a slight sexual dimorphism in adult body shape, the magnitude of which could not be predicted by habitat volume and clarity. A number of comparisons were made to elucidate the possible causes for selection for divergence of adult body shape among Haida Gwaii populations. Body shape of parapatric lake-river stickleback populations differed significantly in concordance with hydrodynamic principles. Comparing the body shape of Haida Gwaii populations to the shape of sympatric benthic-limnetic species pairs from southwestern British Columbia. I found that benthic and limnetic body-shape ecotypes differ by up to 56% of the total variation among Haida Gwaii populations. Tests for phenotypic plasticity of body shape were conducted with two morphologically distinct stickleback populations that had been transplanted into two separate experimental ponds that were the ecological opposites of the respective source lakes. I found evidence for some phenotypic plasticity in body shape; the difference between each source and experimental population was approximately 11% of the total variation in body shape among populations throughout the archipelago. Throughout the islands adult body shape and size can be predicted by both abiotic and biotic factors of the habitat. Populations with derived shape (CV1+), including thicker peduncles, posteriad and closely spaced dorsal spines, anteriad pelvis, short dorsal and anal fins, and smaller body size occur in small, shallow, stained ponds, and populations with less derived shape (CVI-). with smaller narrow peduncles. anteriad and widely spaced dorsal spines. posteriad pelvis. longer dorsal and anal fins, and larger size occur in large, deep. clear lakes. There were large-bodied populations with derived shape (CV2-). including smaller heads and shallower elongate bodies in open water habitats of low productivity, and populations with smaller size and less derived shape (CV2±), with larger heads and deeper bodies, in higher productivity, structurally complex habitats. Populations with robust defensive adaptations have less derived shape (CV1-) and larger size, in response to salmonid predation, while populations with weak defences had derived shape (CV 1+), in response to bird/invertebrate predators. The ecomorphological relationships were consistent between mitochondrial lineages and replicated in each geographical region on the archipelago among geographically distant populations, suggesting the parallel evolution of body shape governed by the hydrodynamic constraints of each habitat. Although initially colonized by ancestors with conserved morphology, the stickleback populations on Haida Gwaii exhibit body shapes suited to the hydrodynamic landscape of the habitat, demonstrating the predictability of natural selection in adaptive radiations.
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    A 100-year retrospective and current carbon budget analysis for the Sooke Lake Watershed: Investigating the watershed-scale carbon implications of disturbance in the Capital Regional District’s water supply lands
    (2015-05-01) Smiley, Byron; Trofymow, J. A.; Niemann, K. O.
    Northern forest ecosystems play an important role in global carbon (C) cycling and are considered to be a net C sink for atmospheric C (IPCC, 2007; Pan, et al., 2011). Reservoir creation is a common cause of deforestation and when coupled with persistent harvest activity that occurs in forest ecosystems, these disturbance events can significantly affect the C budget of a watershed. To understand the effects of these factors on carbon cycling at a landscape level, an examination of forest harvest and reservoir creation was carried out in the watershed of the Sooke Lake Reservoir, the primary water supply for the Greater Victoria area in British Columbia. Covering the period between 1910 and 2012, a detailed disturbance and forest cover dataset was generated for the Sooke Lake Watershed (SLW) and used as input into a spatially-explicit version of the Carbon Budget Model of the Canadian Forest Sector 3 (CBM-CFS3). The model was modified to include export of C out of the forest system in the form of dissolved organic C (DOC) into streams. The fraction of decaying C exported through this mechanism was tuned in the model using DOC measurements from three catchments within the SLW. Site-specific growth and yield curves were also generated for watershed forest stand types, in part, by using LiDAR-derived site indices. C transfers associated with disturbances were adjusted to reflect the disturbance types that occurred during the 100-year study period. Due to the removal of C resulting from wildfire, logging and residue burning, as well as deforestation disturbances, total ecosystem C stocks dropped from 700 metric tonnes of C per hectare (tC ha-1) in 1910 to their current (2012) level of ~550 tC ha-1 across the SLW. Assuming no change in management priorities and negligible effects of climate change, total ecosystem C stocks will not recover to 1910 levels until 2075. The cumulative effect of reservoir creation and expansion on the C budget resulted in 14 tC ha-1 less being sequestered (111,217 tC total) across the watershed by 2012. In contrast, sustained yield forestry within the Capital Regional District’s tenure accounts for a 93 tC ha-1 decrease by 2012, representing an impact six times greater than deforestation associated with reservoir creation. The proportionally greater impact of forestry activity is partly due to current C accounting rules (Intergovernmental Panel on Climate Change) that treats C removed from the forest in the form of Harvested Wood Products as C immediately released to the atmosphere as carbon dioxide. Cumulative DOC export to the Sooke Lake reservoir was ~30,660 tC by 2012, representing a substantial pathway for C leaving the forest ecosystem. However, more research is required to understand what fraction of terrestrially-derived DOC is sequestered long term in lake sediment. The results of this study will assist forest manager decision making on the appropriate management response to future forest disturbance patterns that could result from climate change and to improve climate change mitigation efforts.
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    11 Years and Beyond: A Visual Exploration of Collective Arts for Climate Justice
    (2020-05-25) Gelderman, Hannah; Clover, Darlene
    As we collectively navigate the interconnected climate and inequality crises and fight for a just and habitable future, the arts and creative practices have a critical role to play. In 11 Years and Beyond: A Visual Exploration of Collective Arts for Climate Justice I focus specifically on the role of locally produced, participatory visual arts as a response to both the drivers and the impacts of the climate crisis. From a climate communications perspective participatory visual arts have already proven effective in engaging people in climate solutions (Burke, Ockwell, & Whitmarsh, 2018; Roosen, Klöckner, & Swim, 2018). In addition to improving climate change communications, participatory visual arts offer us a platform to envision a different world (Galafassi et al., 2018), strengthen our activism (Duncombe & Lambert, 2018), build community connection (Berman, 2017), and increase our resiliency (Huss, Kaufman, Avgar & Shuker, 2016) which all help us to navigate, resist and transform our current capitalist, colonial paradigm. Artists, organizers and others who facilitate participatory art projects have an important role to play in these processes, but I have found that there is a lack of resources for those seeking to make change at the intersection of art and activism. To fill this gap I have used arts-based research methods (thus leveraging the power of the arts in my own research) to create Collective Arts for Climate Justice, an illustrated guide in zine format, that advocates for the use of locally produced, participatory visual art practices as a necessary part of our response to our current crises. Because "arts-based forms have the potential to reach wider audiences, including nonacademic audiences" (Leavy & Harris, 2019, p. 216) I have illustrated all my background information (e.g., my literature review), as well as the zines, to ensure that all my research can be as accessible as possible. Through this I hope to invite organizers, artists, and others to utilize community based visual arts to further expand our collective and community capacity to respond to the climate crisis. The growth of participatory art practices can help invigorate and strengthen us as we fight for climate justice, renew our relationships with the land, and build the world we want to live in.
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    13,000 years of fire activity in a temperate rainforest on the Central Coast of British Columbia, Canada
    (2018-04-10) Hoffman, Kira M.; Starzomsk, Brian M.
    While wildfire is globally most common in the savanna-grassland ecotone, the flammability of coastal temperate rainforests is considered low and little is known regarding historic fire activity. Reconstructing historical fire activity typically requires dendrochronological records from fire-scarred trees and post-fire cohorts, but this type of information is rare in perhumid temperate rainforests, which are dominated by dense fuels with high year-round moisture content. I reconstructed historic fire activity using fire scars, tree rings, soil charcoal, and remote sensing techniques in a 2000 km2 island group located within the Hakai Lúxvbálís Conservancy on the coastal margin of central British Columbia. I broadly assessed 13,000 years of fire activity with charcoal deposited in soils, and reconstructed late Holocene fire events with a 700-year chronology built from living fire-scarred trees and stand establishment data. I used a weight of evidence approach to hypothesize the origins of fires and whether First Nations intentionally utilized fire for resource management. Low-severity fires occurred most frequently in forests surrounding former First Nations habitation sites, and lightning strikes do not occur often enough to explain the observed temporal or spatial patterns of fire activity in the study area. Low-severity fires occurred approximately every 39 years, and were 25 times more likely to occur than previously estimated. Fires influenced the composition and structure of vegetation by creating a mosaic of vegetation types in different stages of succession, and thus increased the abundance of culturally important food plants. Fire events have not occurred in the study area since 1893, which also coincides with the reduction of First Nations activities in their traditional territories. My data are consistent with the hypothesis that humans intentionally used fire to manage resources, though further research and ethnographic data collected elsewhere in the region is required to corroborate these findings. Ecological legacies of historic fires remain visible on the present day landscape, and by reconstructing the historic range of fire cycle variability we gain a better understanding of human-driven fire activity and the abrupt changes that occurred in the 20th century.
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    13,000 years of fire history derived from soil charcoal in a British Columbia coastal temperate rain forest
    (Ecosphere, 2016) Hoffman, Kira M.; Gavin, D. G.; Lertzman, K. P.; Smith, D. J.; Starzomski, Brian M.
    Little is known regarding the fire history of high‐latitude coastal temperate rain forests in the Pacific Northwest (PNW) of North America. While reconstructing historical fire regimes typically requires dendrochronological records from fire‐scarred trees or stratigraphically preserved lake sediment data, this type of information is virtually non‐existent in this region. To describe the long‐term fire history of a site on the central coast of British Columbia, Canada, we radiocarbon‐dated 52 pieces of charcoal. Charcoal ages ranged from 12,670 to 70 yr BP. Fires occurred regularly since 12,670 yr BP, with the exception of a distinct fire‐free period at 7500–5500 yr BP. Time since fire (TSF) estimates from soil charcoal and fire‐scarred trees ranged from 12,670 to 100 yr BP (median = 327 yr), and 70% of the sites examined had burned within the past 1000 yr. An increase in fire frequency in the late Holocene is consistent with the widely held hypothesis that anthropogenic fires were common across the PNW. We evaluate TSF distributions and discuss the difficulties in assigning actual fire dates from charcoal fragments with large inbuilt ages in a coastal temperate rain forest setting. We determine that a comprehensive approach using soil charcoal and fire scar analyses is necessary to reconstruct general trends in fire activity throughout the Holocene in this region.
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    13-moment-equations from nonequilibrium thermodynamics and kinetic theory: Comparison for non-linear one-dimensional flows
    (Physics of Fluids, 2025) Bell, Luke; Struchtrup, Henning
    The GENERIC-13 moment equations (general equation for the non-equilibrium reversible-irreversible coupling) [Struchtrup & Öttinger, Phys. Fluids 34, 017105 (2022)] were developed to have complete thermodynamic structure, in contrast to Grad’s 13-moment equations which are not accompanied by a suitable formulation of the second law of thermodynamics and loose hyperbolicity for larger deviations from equilibrium. With GENERIC-13 constructed to agree with Grad-13 to second order in the Knudsen number, both sets are considered and compared for hyperbolicity and plane heat transfer, and Couette and Poiseuille flows. It is shown that the GENERIC-13 equations are unconditionally hyperbolic. Jump and slip boundary conditions for GENERIC-13 are developed from the second law with coefficients adapted from kinetic theory. Additional asymptotically vanishing boundary conditions are constructed such that solutions of the GENERIC-13 equations reduce to those of Grad-13 to second and of Navier–Stokes–Fourier equations to first order in the Knudsen number.
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    15 years of accredited Satir Transformational Systemic Therapy training in the Czech Republic
    (Satir International Journal, 2016) Beránková, Alexandra; Petrovská, Jarmilla
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    16p11.2 haploinsufficiency reduces mitochondrial biogenesis in brain endothelial cells and alters brain metabolism in adult mice
    (Cell Reports, 2023) Béland-Millar, Alexandria; Kirby, Alexia; Truong, Yen; Ouellette, Julie; Yandiev, Sozerko; Bouyakdan, Khalil; Pileggi, Chantal; Naz, Shama; Yin, Melissa; Carrier, Micaël; Kotchetkov, Pavel; St-Pierre, Marie-Kim; Tremblay, Marie-Ève; Courchet, Julien; Harper, Mary-Ellen; Alquier, Thierry; Messier, Claude; Shuhendler, Adam J.; Lacoste, Baptiste
    Summary Neurovascular abnormalities in mouse models of 16p11.2 deletion autism syndrome are reminiscent of alterations reported in murine models of glucose transporter deficiency, including reduced brain angiogenesis and behavioral alterations. Yet, whether cerebrovascular alterations in 16p11.2df/+ mice affect brain metabolism is unknown. Here, we report that anesthetized 16p11.2df/+ mice display elevated brain glucose uptake, a phenomenon recapitulated in mice with endothelial-specific 16p11.2 haplodeficiency. Awake 16p11.2df/+ mice display attenuated relative fluctuations of extracellular brain glucose following systemic glucose administration. Targeted metabolomics on cerebral cortex extracts reveals enhanced metabolic responses to systemic glucose in 16p11.2df/+ mice that also display reduced mitochondria number in brain endothelial cells. This is not associated with changes in mitochondria fusion or fission proteins, but 16p11.2df/+ brain endothelial cells lack the splice variant NT-PGC-1α, suggesting defective mitochondrial biogenesis. We propose that altered brain metabolism in 16p11.2df/+ mice is compensatory to endothelial dysfunction, shedding light on previously unknown adaptative responses.
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    1973, 2002, 2006, and 2010 marsh extent, southern Iraq marshes.
    (2010-04-08T23:00:31Z) Holmes, Keith
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    19th-Century Visions of Prague: Guiding UNESCO Historical Preservation and Urban Development in the City Today
    (2023-03-18) Pacina, Noah
    The Langweil Model of Prague, constructed in the early 19th century, provides an unparalleled perspective of the city. As a UNESCO World Heritage Site, the Historic Centre of Prague remains an exemplary urban space, displaying its rich architectural and visual history for all to see. Ultimately, however, Prague is a living and evolving European capital city. As such, my project seeks to address how the city contends with serious decisions about how cities deal with the problems of today, with heritage integrity and environmental sustainability remaining further heightened issues. To that end, I will engage with the way that the Langweil Model (in particular its modern virtual counterpart) remains at the heart of these issues, as an informing resource for historical preservation and urban development in the city. Furthermore, conclusions on necessary priorities moving forward will be brought to light.
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    A 1D microphysical cloud model for Earth, and Earth-like exoplanets Liquid water and water ice clouds in the convective troposphere
    (Elsevier, 2013) Zsom, Andras; Kaltnegger, Lisa; Goldblatt, Colin
    One significant difference between the atmospheres of stars and exoplanets is the presence of condensed particles (clouds or hazes) in the atmosphere of the latter. In current 1D models clouds and hazes are treated in an approximate way by raising the surface albedo, or adopting measured Earth cloud properties. The former method introduces errors to the modeled spectra of the exoplanet, as clouds shield the lower atmosphere and thus modify the spectral features. The latter method works only for an exact Earth-analog, but it is challenging to extend to other planets. The main goal of this paper is to develop a self-consistent microphysical cloud model for 1D atmospheric codes, which can reproduce some observed properties of Earth, such as the average albedo, surface temperature, and global energy budget. The cloud model is designed to be computationally efficient, simple to implement, and applicable for a wide range of atmospheric parameters for planets in the habitable zone. We use a 1D, cloud-free, radiative-convective, and photochemical equilibrium code originally developed by Kasting, Pavlov, Segura, and collaborators as basis for our cloudy atmosphere model. The cloud model is based on models used by the meteorology community for Earth’s clouds. The free parameters of the model are the relative humidity and number density of condensation nuclei, and the precipitation efficiency. In a 1D model, the cloud coverage cannot be self-consistently determined, thus we treat it as a free parameter. We apply this model to Earth (aerosol number density 100 cm−3, relative humidity 77 %, liquid cloud fraction 40%, and ice cloud fraction 25%) and find that a precipitation efficiency of 0.8 is needed to reproduce the albedo, average surface temperature and global energy budget of Earth. We perform simulations to determine how the albedo and the climate of a planet is influenced by the free parameters of the cloud model. We find that the planetary climate is most sensitive to changes in the liquid water cloud fraction and precipitation efficiency. The advantage of our cloud model is that the cloud height and the droplet sizes are self-consistently calculated, both of which influence the climate and albedo of exoplanets.
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    2 to 1 embeddings of grids into hypercubes
    (1993) Manke, Dennis L.
    We consider two-to-one embeddings of grids into the next smaller Hypercube and derive novel two-to-one embedding techniques that achieve optimal dilation 1 for many grids, where in some cases no previous solutions were known. In particular, dilation 1, two-to-one embeddings into the next smaller Hypercube can be found for grids that are: - square. - close to square. - of height within one of a power of 2.
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    2-D digital filter analysis and application with DEDIP
    (1994) Keddy, William Alfred Lyle
    Two-dimensional (2-0) digital signal processing is applied in many areas including digi­tal image processing, medicine, geography, geology and robotics. In many of these appli­cations 2-D linear, shift invariant (LSI) digital filtering is used and it is desirable to be able to analyze all types of 2-D, LSI filters (finite-duration impulse response (FIR), infi­nite-duration impulse response (IIR) and separable versions of both) and evaluate their performance by applying them to real images. Though many digital image processing (DIP) packages are available, they lack the capability for 2-D filtering beyond simple convolution. The work presented here describes an environment for developing DIP algo­rithms with particular emphasis on the 2-D LSI digital filtering applications. DEDIP, a Developmental Environment for Digital Image Processing, has been developed using the traditional two level programming approach. The low level is a C­-language software library of DIP and system management functions. The high level is a set of digital image processing and file management tools operating under UNIX. Through representation-dependent system management functions, the data and file struc­tures are hidden. These functions perform access and modification, file input and output, and dynamic memory al location on an image which is treated as a single data object. This hides the details of the implementation from the programmer and forms the base of a hierarchical library. The library's top level of DIP functions, built using the system management functions, are data and file structure independent which enhances the portability, reusability and reliability of DEDIP. The DIP algorithms available in DEDIP can be grouped by the operation types of point, intensity and filter. Point operations such as negation and addition of two images are performed on individual pixels. Intensity operations include histogram equalization and linear contrast stretching that modify the histogram of an image. Filter operations include the application of FIR, IIR, separable FIR and separable IIR filter coefficient masks to images as well as the analysis of filter mask characteristics which include the impulse, step, magnitude and phase responses, and the group delays. The capabilities of DEDIP for the implementation of 2-D LSI digital filters are demonstrated through examples of FIR lowpass, IIR lowpass and FIR fan filters, first directional-derivative edge-detection operators and the Laplacian of a Gaussian second­ derivative edge-detection operator. In each example the particular filter coefficient mask is analyzed, the filtering operation on a test image is pe1fo1med and the filtering result is discussed.
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    2-dipath and proper 2-dipath k-colourings
    (2011-05-02) Young, Kailyn M.; MacGillivray, Gary
    A 2-dipath k-colouring of an oriented graph G is an assignment of k colours, 1,2, . . . , k, to the vertices of G such that vertices joined by a directed path of length two are assigned different colours. The 2-dipath chromatic number is the minimum number of colours needed in such a colouring. There are two possible models, depending on whether adjacent vertices must also be assigned different colours. For both models of 2-dipath colouring we develop the basic theory, including characterizing the oriented graphs that can be 2-dipath coloured using a small number of colours, finding bounds on the 2-dipath chromatic number, determining the complexity of deciding the existence of a 2-dipath k-colouring, describing a homomorphism model, and showing how to determine the 2-dipath chromatic number of tournaments and bipartite tournaments.
 
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We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.