This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved that for any finite poset P, the dimension of P is at most half of the number of points in P. We develop some new inequalities for the dimension of finite posets. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d is at least 3, then there is a matching of size d in the comparability graph of P, and a matching of size d in the incomparability graph of P. The bounds in above theorems are best possible, and either result has Hiraguchi's theorem as an immediate corollary. In the second component, we focus on an extremal graph theory problem whose solution relied on the construction of a special kind of posets. In 1959, Paul Erdos, in a landmark paper, proved the existence of graphs with arbitrarily large girth and arbitrarily large chromatic number using probabilistic method. In a 1991 paper of Kriz and Nesetril, they introduced a new graph parameter eye(G). They show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most three. Answering a question of Kriz and Nesetril, we were able to strengthen their results and show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two. The last component is about random posets--the poset version of the Erdos-Renyi random graphs. In 1991, Erdos, Kierstead and Trotter (EKT) investigated random height 2 posets and obtained several upper and lower bounds on the dimension of the random posets. Motivated by some extremal problems involving conditions which force a poset to contain a large standard example, we were compelled to revisit this subject. Our sharpened analysis allows us to conclude that as p approaches 1, the expected value of dimension first increases and then decreases, a subtlety not identified in EKT. Along the way, we establish connections with classical topics in analysis as well as with latin rectangles. Also, using structural insights drawn from this research, we are able to make progress on the motivating extremal problem with an application of the asymmetric form of the Lovasz Local Lemma.

The objective of this study was to see if practicing a lick on the chromatic harmonica could influence or inspire my playing on the diatonic harmonica, and vice versa. The licks I practiced were all in the style of Western Swing. To answer this, I used the following research questions: In what ways can practicing the chromatic harmonica make me a better diatonic harmonica player and vice versa? What are the similarities and differences between the diatonic and the chromatic harmonica in the context of playing Western Swing? What possibilities and limitations does each instrument have when playing Western Swing? The method I used was to record my practicing process and to record two different versions of three tunes. On these three recordings I improvised using both diatonic and chromatic harmonicas. The results showed that, though the differences between the instruments are significant, there is enough common ground to enable an exchange of ideas. The differences were not an obstacle, but a means to find new ways of playing a certain lick. These new ways could then be applied to the other harmonica, creating new variations on licks that I would not have come up with otherwise. Playing the same lick on the two different instruments proved to be an efficient way to learn more about both instruments. Through my method, I was able to become my own teacher and my own muse. I also discovered two distinct sides of me, the chromatic me and the diatonic me.

The generalized deBruijn graph dB(a, k) is the directed graph with a k vertices and edges between vertices x = a1, a 2, ... ak and y = b1, b2, ... b k precisely when a2, ... ak = b1, b2, ... bk-1. The deBruijn graphs can be further generalized by introducing an overlap variable t ≤ k - 1 where the number of consecutive digits by which the vertex labels (sequences) overlap is t. The α-overlap graph is the underlying simple graph of the generalized deBruijn digraph with vertex label overlap 0 < t ≤ k - 1.We denote the α-overlap graph by Gα = G(a, k, t) and the parameters a, k and t are positive integers such that a ≥ 2 and k > t > 0. Thus dB(a, k) = G(a, k, k - 1). In this paper, we show that every a-overlap graph is 3-colorable for any a if k is sufficiently large. We also determine bounds on the chromatic number of the α-overlap graphs if a is much larger than k.

The presence of various impairments in fiber channel has forced researchers to uncover solutions to minimize those effects. With the advancement of technology, optical solutions were finally easier to implement in the system. To this day, optical compensation methods are still found to be as the best way to minimize fiber impairments. With the development of digital signal processing (DSP) and FIR techniques, coherent detection with digital signal processing (DSP) is developed, analyzed theoretically and numerically and experimentally demonstrated in long-haul high speed fiber‐optic transmission system. The use of DSP in conjunction with coherent detection unleashes the benefits of coherent detection which rely on the preservation of full information of the transmitted field. These benefits include high receiver sensitivity, the ability to achieve high spectral‐efficiency and the use of advanced modulation formats. The local oscillator (LO) of coherent receiver alleviates the need for hardware phase‐locking and polarization tracking, which can now be achieved in the digital domain. The computational complexity previously associated with coherent detection is hence significantly diminished and coherent detection is once again considered a feasible detection alternative. In this thesis, an optical fiber communication scheme using the coherent detection method is simulated. Firstly, at the beginning of each chapter, we introduce the various compensation methods for certain optical fiber impairments which is developed by the pioneers. However, such technique does introduce enormous complexity to the system, in addition to a large cost. For that reason, the main focus had to shift to an alternative method. DSP techniques has enabled simple techniques to mitigate various impairments in fiber-optical systems. In this thesis, the background knowledge about the structure of fiber-optical transmission system is provided. After the mathematical analysis of the various impairments (laser noise, chromatic dispersion, polarization mode dispersion and nonlinearity) in fiber-optical links, the compensation methods by using DSP techniques are provided. By the methods of fourth-power carrier recovery algorithm and feedforward carrier recovery algorithm, the phase rotation in constellation due to laser noise is compensated in QPSK systems and QAM systems, respectively. The feedforward carrier recovery algorithm has a high tolerance for laser linewidth in high-order QAM system. As for PMD compensation, on the basis of adaptive equalizers in both time domain and frequency domain achiever by the pioneers, a novel LMS algorithm is proposed in this thesis. It has a fair comparative and steady computational complexity with the increase in the number of training blocks. The last part is the nonlinearity compensation. The DBP compensation is a popular method for nonlinearity compensation but its computational complexity is fair high (Shao J, Kumar S and Liang X., 2013). We adopt two kinds of fold-DBP which are distance-folded DBP and dispersion-folded DBP to compensate the joint impairments of chromatic dispersion and nonlinearity in dispersion-managed system. The distance-folded DBP works well in the full compensation dispersion-managed system but in the presence of RDPS, only the dispersion-folded DBP is efficient. / Thesis / Master of Applied Science (MASc)

In this piece, I have looked to use art in an attempt to explore a known phenomenon of the visual system: in this case, chromatic adaptation. The name delta in this sense has two meanings. The first is that of the mathematical symbol Δ used to represent change. This refers to not only the changing light in the art piece but the hopeful change in the viewer as they walk away questioning what it is they saw and what they see. The second refers to the landmass that occurs when a flowing body of water meets a still one, such as a river into an ocean. Through this process it has become evident that the knowledge gained is not as important as the questions asked; I now stand on the last bit of dry land before wading into the endless ocean of questions. The focus of this work has been on experience, perception, and presence. It has become clear that, while a viewer may not see change, they do feel that change. The question then becomes how do we become more attuned and adept at recognizing these feelings, what are the implications of doing so, and why does that even matter.

No description available.

No / Precortical color vision is mediated by three independent opponent or cardinal mechanisms that linearly combine receptoral outputs to form L/M, S/(L+M), and L+M channels. However, data from a variety of psychophysical and physiological experiments indicate that chromatic processing undergoes a reorganization away from the basic opponent model. Frequently, this post-opponent reorganization is viewed in terms of the generation of multiple ¿higher order¿ chromatic mechanisms, tuned to a wide variety of axes in color space. Moreover, adaptation experiments have revealed that the synthesis of these mechanisms occurs at a level in the cortex following the binocular integration of the inputs from each eye. Here we report results from an experiment in which the influence of chromatic adaptation on the perceived visual location of a test stimulus was explored using a Vernier alignment task. The results indicate that not only is positional information processed independently within the L/M, S/(L+M), and L+M channels, but that when adapting and test stimuli are extended to non-cardinal axes, the existence of multiple chromatically tuned mechanisms is revealed. Most importantly, the effects of chromatic adaptation on this task exhibit little interocular transfer and have rapid decay rates, consistent with chromatic as opposed to contrast adaptation. These findings suggest that the reorganization of chromatic processing may take place earlier in the visual pathway than previously thought.

We study graph parameters arising from different types of colourings of random graphs, defined broadly as an assignment of colours to either the vertices or the edges of a graph. The chromatic number X(G) of a graph is the minimum number of colours required for a vertex colouring where no two adjacent vertices are coloured the same. Determining the chromatic number is one of the classic challenges in random graph theory. In Chapter 3, we give new upper and lower bounds for the chromatic number of the dense random graph G(n,p)) where p &isin; (0,1) is constant. These bounds are the first to match up to an additive term of order o(1) in the denominator, and in particular, they determine the average colour class size in an optimal colouring up to an additive term of order o(1). In Chapter 4, we study a related graph parameter called the equitable chromatic number. This is defined as the minimum number of colours needed for a vertex colouring where no two adjacent vertices are coloured the same and, additionally, all colour classes are as equal in size as possible. We prove one point concentration of the equitable chromatic number of the dense random graph G(n,m) with m = pn(n-1)/2, p &LT; 1-1/e² constant, on a subsequence of the integers. We also show that whp, the dense random graph G(n,p) allows an almost equitable colouring with a near optimal number of colours. We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, which is a path where no colour is repeated. The least number of colours where this is possible is called the rainbow connection number rc(G). Since its introduction in 2008 as a new way to quantify how well connected a given graph is, the rainbow connection number has attracted the attention of a great number of researchers. For any graph G, rc(G)&ge;diam(G), where diam(G) denotes the diameter. In Chapter 5, we will see that in the random graph G(n,p), rainbow connection number 2 is essentially equivalent to diameter 2. More specifically, we consider G ~ G(n,p) close to the diameter 2 threshold and show that whp rc(G) = diam(G) &isin; {2,3}. Furthermore, we show that in the random graph process, whp the hitting times of diameter 2 and of rainbow connection number 2 coincide. In Chapter 6, we investigate sharp thresholds for the property rc(G)&le;=r where r is a fixed integer. The results of Chapter 6 imply that for r=2, the properties rc(G)&le;=2 and diam(G)&le;=2 share the same sharp threshold. For r&ge;3, the situation seems quite different. We propose an alternative threshold and prove that this is an upper bound for the sharp threshold for rc(G)&le;=r where r&ge;3.

No description available.

The eye is our window to the world. Human vision has therefore been extensively studied over the years. However, in-depth studies are often either limited to our central visual field, or, when extended to the periphery, only correct optical errors related to a narrow spectrum of light. This thesis extends the current knowledge by considering the full visible spectrum over a wide visual field. A broad spectrum means that the wavelength dependence of light propagation inside the eye has to be considered; the optics of the eye will therefore not form a retinal image in the same location for all wavelengths, a phenomenon called chromatic aberration. We present here a new methodology to objectively measure the magnitude of transverse chromatic aberration (TCA) across the visual field of the human eye, and show that the ocular TCA increases linearly with off-axis angle (about 0.21 arcmin per degree for the spectral range from 543 nm to 842 nm). Moreover, we have implemented adaptive psychophysical methods to quantify the impact of TCA on central and peripheral vision. We have found that inducing additional TCA degrades peripheral grating detection acuity more than foveal resolution acuity (more than 0.05 logMAR per arcmin of induced TCA peripherally compared to 0.03 logMAR/arcmin foveally). As stimuli to evaluate peripheral vision, we recommend gratings that are obliquely-oriented relative to the visual field meridian. The results of this thesis have clinical relevance for improving peripheral vision and are equally important for retinal imaging techniques. To limit the negative impacts of TCA on vision, inducing additional TCA should be avoided when the peripheral refractive errors are to be corrected, such as for people suffering from macular degeneration and central visual field loss. In retinal imaging applications, TCA leads to lateral offsets when imaging is performed in more than one wavelength. Consequently, the measurement of TCA together with careful pupil alignment and subsequent compensation can improve the functionality of these instruments. / Ögat är vårt fönster mot världen, och syn har mätts och studerats i stor utsträckning över åren. Trots detta är forskningen om mänsklig syn oftast begränsad till det centrala synfältet, och i studier av det perifera synfältet korrigeras optiska fel endast över ett smalt våglängdsområde. Denna avhandling vidgar forskningen om vår syn till att inkludera hela det synliga spektrumet över ett stort synfält. Ett brett spektrum innebär att vi måste ta hänsyn till våglängdsberoendet i ljusets brytning i ögat; ögats optik kan därför inte avbilda ett objekt till samma bildläge på näthinnan för alla våglängder, ett fenomen som kallas kromatisk aberration. Vi presenterar här en ny metod för att mäta mängden transversell kromatisk aberration (TCA) över ögats synfält och visar att ögats TCA ökar linjärt med vinkeln ut i synfältet (ungefär 0,21 bågminuter per grad från 543 nm till 842 nm). Dessutom har vi implementerat adaptiva psykofysiska mätmetoder för att kvantifiera effekten av TCA på central och perifer syn. Våra resultat visar att extra inducerad TCA påverkar den perifera förmågan att upptäcka sinusformade randmönster mer än den centrala förmågan att upplösa motsvarande ränder (mer än 0,05 logMAR per bågminut inducerad TCA i periferin jämfört med 0,03 logMAR/bågminut centralt). Vid utvärdering av perifer syn rekommenderar vi att använda sinusformade randmönster med en sned riktning jämfört med synfältsmeridianen. Resultaten som presenteras i avhandlingen har klinisk betydelse för att förbättra den perifera synen och är även viktiga för tekniker som avbildar ögats näthinna. För att begränsa den negativa effekt TCA har på synen ska man undvika att inducera extra TCA, t.e.x. när ögats perifera refraktiva fel korrigeras med glasögon för människor med makula degeneration och centralt synfältsbortfall. Vid avbildning av näthinnan ger ögats TCA förskjutningar mellan bilder i olika våglängder. Därför kan mätningar av TCA, tillsammans med välkontrollerad linjering av pupillens position och efterföljande kompensation, förbättra funktionen hos dessa instrument. / <p>QC 20160511</p>